{"id":59,"date":"2026-02-20T05:09:00","date_gmt":"2026-02-20T05:09:00","guid":{"rendered":"https:\/\/oualator.com\/measure\/?p=59"},"modified":"2026-02-21T07:24:50","modified_gmt":"2026-02-21T07:24:50","slug":"power-series-calculator","status":"publish","type":"post","link":"https:\/\/oualator.com\/measure\/power-series-calculator\/","title":{"rendered":"Power Series Calculator | Expand Functions into Series"},"content":{"rendered":"\n<div class=\"bg-white rounded-lg shadow-lg p-6 mb-8\">  \n    <div class=\"mb-8\">\n      <p class=\"text-gray-600\">\n        A <span class=\"font-medium\">Power Series Calculator with Step-by-Step Solutions<\/span> helps you expand mathematical\n        functions into infinite series quickly and accurately. Whether you\u2019re working on calculus homework, preparing for exams,\n        or exploring advanced mathematical analysis, this tool simplifies complex\n        <a class=\"text-blue-600 hover:underline\" href=\"https:\/\/en.wikipedia.org\/wiki\/Taylor_series\" target=\"_blank\" rel=\"noopener noreferrer\">Taylor series<\/a>\n        and\n        <a class=\"text-blue-600 hover:underline\" href=\"https:\/\/en.wikipedia.org\/wiki\/Taylor_series#Maclaurin_series\" target=\"_blank\" rel=\"noopener noreferrer\">Maclaurin series<\/a>\n        expansions while clearly showing each step of the process.\n      <\/p>\n      <p class=\"text-gray-600 mt-3\">\n        Instead of manually computing derivatives and plugging values into formulas, the calculator instantly provides structured\n        results\u2014saving time and reducing errors. It also helps students better understand how infinite series behave, especially\n        when studying convergence and approximation techniques. <p class=\"text-gray-600 mt-3\">\n  Instead of manually computing derivatives and plugging values into formulas, the calculator instantly provides structured\n  results\u2014saving time and reducing errors. It also helps students better understand how infinite series behave, especially\n  when studying convergence and approximation techniques. Try the \n  <a href=\"https:\/\/oualator.com\/measure\/harmonic-series-calculator\/\" \n     class=\"text-blue-600 hover:underline\">\n    Harmonic Series Calculator\n  <\/a> \n  for quick insights into series behavior.\n<\/p>\n      <\/p>\n    <\/div>\n<\/div>\n\n\n\n<div class=\"bg-white rounded-lg shadow-lg p-6 mb-8\">\n  <div class=\"max-w-4xl mx-auto\">\n\n    <div class=\"flex items-start justify-between gap-4 mb-4\">\n      <p class=\"text-xl md:text-2xl font-bold text-gray-900\">\n        Table of Contents\n      <\/p>\n    <\/div>\n\n    <div class=\"bg-gray-50 border border-gray-100 rounded-lg p-5\">\n      <p class=\"text-gray-600 text-sm mb-4\">\n        Use these links to quickly navigate the page.\n      <\/p>\n\n      <ul class=\"space-y-2 text-gray-800\">\n        <li>\n          <a class=\"text-blue-600 hover:underline\" href=\"#what-is-power-series\">\n            What is a Power Series?\n          <\/a>\n        <\/li>\n        <li>\n          <a class=\"text-blue-600 hover:underline\" href=\"#how-to-use\">\n            How to Use the Power Series Calculator\n          <\/a>\n        <\/li>\n        <li>\n          <a class=\"text-blue-600 hover:underline\" href=\"#convergence\">\n            Understanding Radius and Interval of Convergence\n          <\/a>\n          <ul class=\"mt-2 ml-5 space-y-1 text-sm text-gray-700 list-disc\">\n            <li>\n              <a class=\"text-blue-600 hover:underline\" href=\"#convergence\">\n                Radius of Convergence (R)\n              <\/a>\n            <\/li>\n            <li>\n              <a class=\"text-blue-600 hover:underline\" href=\"#convergence\">\n                Interval of Convergence\n              <\/a>\n            <\/li>\n            <li>\n              <a class=\"text-blue-600 hover:underline\" href=\"#convergence\">\n                Ratio Test\n              <\/a>\n            <\/li>\n          <\/ul>\n        <\/li>\n        <li>\n          <a class=\"text-blue-600 hover:underline\" href=\"#common-expansions\">\n            Common Power Series Expansions (Maclaurin Series)\n          <\/a>\n        <\/li>\n        <li>\n          <a class=\"text-blue-600 hover:underline\" href=\"#example\">\n            Step-by-Step Example: Expansion of 1\/(1\u2212x)\n          <\/a>\n        <\/li>\n        <li>\n          <a class=\"text-blue-600 hover:underline\" href=\"#why-use\">\n            Why Use a Power Series Calculator with Steps?\n          <\/a>\n        <\/li>\n        <li>\n          <a class=\"text-blue-600 hover:underline\" href=\"#final-thoughts\">\n            Final Thoughts\n          <\/a>\n        <\/li>\n        <li>\n          <a class=\"text-blue-600 hover:underline\" href=\"#faqs\">\n            FAQs\n          <\/a>\n        <\/li>\n      <\/ul>\n\n    <\/div>\n\n  <\/div>\n<\/div>\n\n\n\n<link href=\"https:\/\/cdn.jsdelivr.net\/npm\/tailwindcss@2.2.19\/dist\/tailwind.min.css\" rel=\"stylesheet\">\n  <!-- Chart.js -->\n  <script src=\"https:\/\/cdn.jsdelivr.net\/npm\/chart.js@4.4.3\/dist\/chart.umd.min.js\"><\/script>\n  <!-- Font Awesome for icons -->\n  <link rel=\"stylesheet\" href=\"https:\/\/cdn.jsdelivr.net\/npm\/@fortawesome\/fontawesome-free@6.5.2\/css\/all.min.css\">\n  <!-- Google Fonts -->\n  <link rel=\"stylesheet\" href=\"https:\/\/cdn.jsdelivr.net\/npm\/@fontsource\/roboto@3.3.1\/400.css\">\n  <style>\n    body {\n      font-family: 'Roboto', Arial, sans-serif;\n      background: #f9fafb;\n      color: #1a202c;\n    }\n    .no-scrollbar::-webkit-scrollbar {\n      display: none;\n    }\n    .no-scrollbar {\n      -ms-overflow-style: none;\n      scrollbar-width: none;\n    }\n    \/* Optimize for print\/PDF *\/\n    @media print {\n      .no-scrollbar, .overflow-x-auto, .overflow-y-auto {\n        overflow: visible !important;\n      }\n      input, textarea, select, button {\n        color: #1a202c !important;\n        background: none !important;\n        border: none !important;\n      }\n    }\n    .chart-container {\n      position: relative;\n      width: 100%;\n      height: 400px;\n      margin-top: 1rem;\n    }\n    @media (max-width: 770px) {\n      .chart-container { height: 250px; }\n    }\n  <\/style>\n\n\n  <header class=\"max-w-3xl mx-auto mb-8\">\n    <h2 class=\"text-4xl sm:text-5xl font-bold mb-3 text-blue-600 flex items-center gap-2\">\n      <i class=\"fas fa-infinity\"><\/i> Power Series Calculator\n    <\/h2>\n    <div class=\"bg-blue-50 border-l-4 border-blue-400 p-4 rounded-lg shadow-sm text-base\">\n      <p>\n        <b>Power series<\/b> represent functions as sums of infinite polynomials which net result is centered about a point.\n        The general form is:<br>\n        <span class=\"text-gray-700 text-lg italic\">f(x) = <span class=\"text-blue-700 font-mono\">\u2211<sub>n=0<\/sub><sup>\u221e<\/sup> a\u2099(x-c)\u207f<\/span><\/span>\n      <\/p>\n      <ul class=\"list-disc list-inside mt-2 text-gray-700\">\n        <li><b>Input<\/b> any analytical function and compute its power series expansion about a point <i>c<\/i>.<\/li>\n        <li>\n          <b>See<\/b> the resulting polynomial approximation, the exact and approximated graphs,\n          and coefficient table.\n        <\/li>\n        <li>\n          <em>Great for students and educators studying Taylor series, Maclaurin series, function approximations, and calculus!<\/em>\n        <\/li>\n      <\/ul>\n    <\/div>\n  <\/header>\n\n  <main class=\"max-w-3xl mx-auto bg-white rounded-lg shadow-lg p-6\">\n\n    <section class=\"mb-6\">\n      <h2 class=\"text-2xl font-semibold mb-2\"><i class=\"fas fa-edit\"><\/i> Power Series Input<\/h2>\n      <form id=\"seriesForm\" class=\"grid grid-cols-1 md:grid-cols-3 gap-4 items-end\">\n        <div>\n          <label class=\"block font-medium mb-1\" for=\"functionInput\">Function f(x):<\/label>\n          <input\n            id=\"functionInput\"\n            name=\"function\"\n            type=\"text\"\n            class=\"w-full border-gray-300 rounded px-3 py-2 text-base\"\n            value=\"sin(x)\"\n            placeholder=\"Example: exp(-x^2) or sin(x)\"\n            required\n            autocomplete=\"off\"\n          >\n        <\/div>\n        <div>\n          <label class=\"block font-medium mb-1\" for=\"centerInput\">Center (c):<\/label>\n          <input\n            id=\"centerInput\"\n            name=\"center\"\n            type=\"number\"\n            class=\"w-full border-gray-300 rounded px-3 py-2\"\n            value=\"0\"\n            step=\"any\"\n            required\n          >\n        <\/div>\n        <div>\n          <label class=\"block font-medium mb-1\" for=\"degreeInput\">Degree (N):<\/label>\n          <input\n            id=\"degreeInput\"\n            name=\"degree\"\n            type=\"number\"\n            min=\"1\"\n            max=\"50\"\n            class=\"w-full border-gray-300 rounded px-3 py-2\"\n            value=\"6\"\n            required\n          >\n        <\/div>\n        <div class=\"col-span-1 md:col-span-3 flex gap-3 mt-3\">\n          <button type=\"submit\"\n            class=\"bg-blue-600 text-white font-bold py-2 px-6 rounded shadow flex items-center gap-2 hover:bg-blue-700 transition-colors duration-150\"\n          >\n            <i class=\"fas fa-calculator\"><\/i> Calculate\n          <\/button>\n          <button type=\"button\"\n            class=\"bg-gray-200 text-gray-700 font-semibold py-2 px-4 rounded flex items-center gap-2 hover:bg-gray-300 transition-colors\"\n            onclick=\"resetForm()\"\n          >\n            <i class=\"fas fa-undo\"><\/i> Reset\n          <\/button>\n        <\/div>\n      <\/form>\n    <\/section>\n\n    <div id=\"resultsSection\" class=\"mt-10\">\n      <section class=\"\">\n        <div id=\"seriesSummary\" class=\"mb-6\"><\/div>\n        <div class=\"grid grid-cols-1 md:grid-cols-2 gap-8\">\n          <div>\n            <h3 class=\"font-semibold text-lg mb-1\"><i class=\"fas fa-table\"><\/i> Coefficient Table (a\u2099)<\/h3>\n            <div class=\"overflow-x-auto no-scrollbar\">\n              <table id=\"coeffTable\" class=\"min-w-full text-sm border border-gray-200 rounded\">\n                <thead>\n                  <tr class=\"bg-gray-50\">\n                    <th class=\"border-b px-3 py-2 text-left\">n<\/th>\n                    <th class=\"border-b px-3 py-2 text-left\">a\u2099<\/th>\n                  <\/tr>\n                <\/thead>\n                <tbody>\n                  <!-- Results injected here -->\n                <\/tbody>\n              <\/table>\n            <\/div>\n\n            <div id=\"seriesExpression\" class=\"mt-6 text-base\"><\/div>\n          <\/div>\n          <div>\n            <h3 class=\"font-semibold text-lg mb-2\"><i class=\"fas fa-chart-line\"><\/i> Function &#038; Series Graph<\/h3>\n            <div class=\"chart-container bg-gray-50 rounded border\"><canvas id=\"seriesChart\"><\/canvas><\/div>\n            <label class=\"block mt-3 text-sm\">Graph Range: <span id=\"rangeLabel\">x \u2208 [ -8, 8 ]<\/span><\/label>\n            <input type=\"range\" min=\"2\" max=\"20\" value=\"8\" step=\"0.5\" id=\"graphRangeSlider\" class=\"w-full\">\n          <\/div>\n        <\/div>\n      <\/section>\n    <\/div>\n  <\/main>\n\n  <!-- Math.js (for symbolic\/math evaluation) -->\n  <script src=\"https:\/\/cdn.jsdelivr.net\/npm\/mathjs@11.11.1\/lib\/browser\/math.js\"><\/script>\n\n  <script>\n    \/\/ Helper for formatting coefficients and terms\n    function formatTerm(a, n, c, showSign=false) {\n      if (Math.abs(a) < 1e-14) return '';\n      let strA = math.format(a, { precision: 7 });\n      let sign = (a >= 0 && showSign) ? ' + ' : (a < 0 ? ' - ' : '');\n      let coeff = (n === 0 || Math.abs(a) !== 1) ? Math.abs(a).toPrecision(5).replace(\/\\.?0+$\/,'') : '';\n      if(n===0) return `${sign}${coeff}`;\n      let xPart = '(x'+(c==0?'':('-'+c))+')'+(n>1?`^${n}`:'');\n      return `${sign}${coeff ? coeff + '*' : ''}${xPart}`;\n    }\n\n    \/\/ Derivative and Taylor coefficient calculation\n    function taylorCoefficients(expr, c, degree) {\n      const coefficients = [];\n      let compiled = null;\n      try {\n        compiled = math.parse(expr);\n      } catch (e) {\n        return {error: 'Unable to parse function expression. Please review your input.'};\n      }\n      for(let n=0; n<=degree; n++) {\n        \/\/ n-th derivative at x = c, divided by n!\n        let deriv = compiled;\n        for(let i=0; i<n; i++) {\n          deriv = math.derivative(deriv, 'x');\n        }\n        let evaluated;\n        try {\n          evaluated = deriv.evaluate({x: c});\n        } catch(e) {\n          return {error: `Unable to evaluate the ${n}${n==1?'st':n==2?'nd':n==3?'rd':'th'} derivative at x = ${c}.`};\n        }\n        let coeff = evaluated \/ math.factorial(n);\n        coefficients.push(coeff);\n      }\n      return {coefficients};\n    }\n\n    \/\/ Evaluate polynomial with power series coefficients at given x\n    function evaluateSeries(coefficients, c, x) {\n      let sum = 0;\n      for(let n=0; n<coefficients.length; n++) {\n        sum += coefficients[n] * Math.pow(x-c, n);\n      }\n      return sum;\n    }\n\n    \/\/ Render the coefficient table\n    function renderTable(coefficients) {\n      let html = '', digits = 7;\n      coefficients.forEach((a, n) => {\n        html += `<tr class=\"${n%2===0?'bg-white':'bg-gray-50'}\">\n          <td class=\"border-b px-3 py-2\">${n}<\/td>\n          <td class=\"border-b px-3 py-2 font-mono\">${math.format(a,{precision: digits})}<\/td>\n        <\/tr>`;\n      });\n      document.getElementById('coeffTable').querySelector('tbody').innerHTML = html;\n    }\n\n    \/\/ Render the series expression\n    function renderSeriesExpr(coeffs, c) {\n      let expr = '';\n      coeffs.forEach((a, n) => {\n        expr += formatTerm(a, n, c, n>0);\n      });\n      expr = expr.trim().replace(\/^\\+ \/,'');\n      document.getElementById('seriesExpression').innerHTML =\n        `<div class=\"text-sm text-gray-600 italic mt-1\">Power Series:<\/div>\n        <span class=\"font-mono text-blue-700 text-lg\">f(x) \u2248 ${expr || '...'}<\/span>`;\n    }\n\n    \/\/ Render function and power series graphs with Chart.js\n    let chartInstance;\n    function drawChart(coeffs, func, c, xMin, xMax) {\n      let points = 201;\n      let xVals = [], fx = [], sx = [];\n      let error = false;\n      for(let i=0;i<points;i++) {\n        let x = xMin + (xMax-xMin)*i\/(points-1);\n        xVals.push(x);\n        let y1, y2;\n        try {\n          y1 = func.evaluate({x: x});\n        } catch(e){ y1 = NaN; error = true; }\n        try {\n          y2 = evaluateSeries(coeffs, c, x);\n        } catch(e){ y2 = NaN; }\n        fx.push(y1);\n        sx.push(y2);\n      }\n      if(chartInstance) chartInstance.destroy();\n      chartInstance = new Chart(document.getElementById('seriesChart').getContext('2d'), {\n        type: 'line',\n        data: {\n          labels: xVals,\n          datasets: [\n            {\n              label: 'Exact f(x)',\n              data: fx,\n              borderColor: 'rgba(59,130,246,0.8)',\n              fill: false,\n              pointRadius: 0,\n              tension: 0.1,\n              borderWidth: 2,\n            },\n            {\n              label: 'Series approx.',\n              data: sx,\n              borderColor: 'rgba(16,185,129,0.86)',\n              borderDash: [7,3],\n              fill: false,\n              pointRadius: 0,\n              tension: 0.1,\n              borderWidth: 2,\n            },\n          ]\n        },\n        options: {\n          responsive: true,\n          animation: false,\n          plugins: {\n            legend: { display: true, position: 'top' },\n            tooltip: { enabled: true, mode: 'nearest', intersect: false },\n          },\n          scales: {\n            x: { title: { display: true, text: 'x' }, grid: {display: false}},\n            y: { title: { display: true, text: 'y' }, grid: { color: '#ececec'} }\n          },\n        }\n      });\n    }\n\n    \/\/ Summary above results\n    function renderSummary(fstr, c, n) {\n      document.getElementById('seriesSummary').innerHTML =\n        `<div class=\"bg-green-50 border-l-4 border-green-400 text-green-700 p-3 pr-8 mb-1 rounded flex items-center gap-3\">\n          <span><i class=\"fas fa-info-circle\"><\/i><\/span>\n          <span>\n            <b>Function:<\/b> <span class=\"font-mono text-blue-700\">${fstr}<\/span> &nbsp; &bull; &nbsp;\n            <b>Expansion center:<\/b> <span class=\"font-mono\">${c}<\/span> &nbsp; &bull; &nbsp;\n            <b>Degree:<\/b> <span class=\"font-mono\">${n}<\/span>\n          <\/span>\n        <\/div>`;\n    }\n\n    \/\/ Main event handler\n    function calculateAndDisplay() {\n      \/\/ Collect input\n      let fstr = document.getElementById('functionInput').value.trim();\n      let c = parseFloat(document.getElementById('centerInput').value);\n      let n = parseInt(document.getElementById('degreeInput').value, 10);\n\n      \/\/ 1. Coefficient calculation\n      let res = taylorCoefficients(fstr, c, n);\n      if(res.error) {\n        document.getElementById('seriesSummary').innerHTML =\n          `<div class=\"bg-red-50 border-l-4 border-red-400 text-red-700 p-2 pr-6 mb-2 rounded text-base\">\n            <i class=\"fas fa-exclamation-triangle\"><\/i> ${res.error}\n          <\/div>`;\n        document.getElementById('coeffTable').querySelector('tbody').innerHTML = '';\n        document.getElementById('seriesExpression').innerHTML = '';\n        if(chartInstance){ chartInstance.destroy(); }\n        return;\n      }\n      let coeffs = res.coefficients;\n      renderSummary(fstr, c, n);\n      renderTable(coeffs);\n      renderSeriesExpr(coeffs, c);\n\n      \/\/ 2. Compile function\n      let compiled;\n      try { compiled = math.compile(fstr); }\n      catch {\n        document.getElementById('seriesSummary').innerHTML +=\n          `<div class=\"text-yellow-700 italic\">Unable to plot function due to parse error.<\/div>`;\n        if(chartInstance){ chartInstance.destroy(); }\n        return;\n      }\n      \/\/ 3. Draw the chart (initially with current slider range)\n      let xSpan = parseFloat(document.getElementById('graphRangeSlider').value);\n      drawChart(coeffs, compiled, c, c-xSpan, c+xSpan);\n    }\n\n    \/\/ Slider handler for range\n    document.getElementById('graphRangeSlider').addEventListener('input', function() {\n      let xSpan = parseFloat(this.value);\n      let fstr = document.getElementById('functionInput').value.trim();\n      let c = parseFloat(document.getElementById('centerInput').value);\n      let n = parseInt(document.getElementById('degreeInput').value, 10);\n      let res = taylorCoefficients(fstr, c, n);\n      if(!res.coefficients || !fstr) return;\n      let coeffs = res.coefficients;\n      let compiled;\n      try { compiled = math.compile(fstr); }\n      catch { return; }\n      drawChart(coeffs, compiled, c, c-xSpan, c+xSpan);\n      document.getElementById('rangeLabel').textContent = `x \u2208 [ ${math.format(c-xSpan,{precision:3})}, ${math.format(c+xSpan,{precision: 3})} ]`;\n    });\n\n    \/\/ Reset form handler\n    function resetForm() {\n      document.getElementById('functionInput').value = 'sin(x)';\n      document.getElementById('centerInput').value = 0;\n      document.getElementById('degreeInput').value = 6;\n      document.getElementById('graphRangeSlider').value = 8;\n      document.getElementById('rangeLabel').textContent = 'x \u2208 [ -8, 8 ]';\n      calculateAndDisplay();\n    }\n\n    \/\/ Form submit: prevent reload\n    document.getElementById('seriesForm').addEventListener('submit', function(e){\n      e.preventDefault(); calculateAndDisplay();\n    });\n\n    \/\/ Initial calculation\/setup\n    window.onload = function() { calculateAndDisplay(); };\n\n  <\/script>\n\n\n\n<!-- What is a Power Series -->\n<div id=\"what-is-power-series\" class=\"mb-10\">\n  <h3 class=\"text-xl font-semibold text-gray-900 mb-3\">\n    What is a Power Series?\n  <\/h3>\n  <div class=\"bg-gray-50 border border-gray-100 rounded-lg p-4\">\n    <p class=\"text-gray-700\">\n      A <a class=\"text-blue-600 hover:underline\" href=\"https:\/\/en.wikipedia.org\/wiki\/Power_series\" target=\"_blank\" rel=\"noopener noreferrer\">power series<\/a>\n      is a special type of infinite series that represents a function as an infinite polynomial. Instead of using a finite\n      number of terms like standard polynomials, a power series continues indefinitely, allowing it to approximate complex\n      functions such as exponential, trigonometric, and logarithmic expressions.\n    <\/p>\n\n    <div class=\"mt-4\">\n      <div class=\"text-sm text-gray-500 mb-2\">General form:<\/div>\n      <pre class=\"bg-gray-900 text-gray-100 rounded-lg p-4 overflow-x-auto text-sm\"><code><span class=\"wp-katex-eq\" data-display=\"false\">\\sum_{n=0}^{\\infty} c_n (x - a)^n<\/span><\/code><\/pre>\n    <\/div>\n\n    <div class=\"grid grid-cols-1 md:grid-cols-3 gap-3 mt-4 text-sm\">\n      <div class=\"bg-white rounded-lg border border-gray-100 p-3\">\n        <div class=\"font-semibold text-gray-900 mb-1\"><span class=\"wp-katex-eq\" data-display=\"false\">c_n<\/span><\/div>\n        <div class=\"text-gray-600\">Coefficients that determine the size of each term<\/div>\n      <\/div>\n      <div class=\"bg-white rounded-lg border border-gray-100 p-3\">\n        <div class=\"font-semibold text-gray-900 mb-1\"><span class=\"wp-katex-eq\" data-display=\"false\">x<\/span><\/div>\n        <div class=\"text-gray-600\">The variable<\/div>\n      <\/div>\n      <div class=\"bg-white rounded-lg border border-gray-100 p-3\">\n        <div class=\"font-semibold text-gray-900 mb-1\"><span class=\"wp-katex-eq\" data-display=\"false\">a<\/span><\/div>\n        <div class=\"text-gray-600\">Center of the series (expansion point)<\/div>\n      <\/div>\n    <\/div>\n\n    <p class=\"text-gray-700 mt-4\">\n      When the center is <span class=\"wp-katex-eq\" data-display=\"false\">a = 0<\/span>, the result is called a\n      <a class=\"text-blue-600 hover:underline\" href=\"https:\/\/en.wikipedia.org\/wiki\/Taylor_series#Maclaurin_series\" target=\"_blank\" rel=\"noopener noreferrer\">Maclaurin series<\/a>.\n      Power series are powerful because within a certain range of values, they behave exactly like the original function.\n      This enables approximation, solving differential equations, and real-world modeling.\n    <\/p>\n  <\/div>\n<\/div>\n\n<!-- How to Use -->\n<div id=\"how-to-use\" class=\"mb-10\">\n  <h3 class=\"text-xl font-semibold text-gray-900 mb-3\">\n    How to Use the Power Series Calculator\n  <\/h3>\n\n  <div class=\"grid grid-cols-1 md:grid-cols-2 gap-4\">\n    <div class=\"rounded-lg border border-gray-100 p-5 bg-white\">\n      <div class=\"flex items-start gap-3\">\n        <div class=\"flex-shrink-0 w-9 h-9 rounded-full bg-blue-600 text-white flex items-center justify-center font-bold\">1<\/div>\n        <div>\n          <h4 class=\"font-semibold text-gray-900 mb-1\">Enter the Function<\/h4>\n          <p class=\"text-gray-600 text-sm\">Type the function you want to expand, such as:<\/p>\n          <ul class=\"list-disc pl-5 mt-2 text-sm text-gray-700 space-y-1\">\n            <li><code class=\"bg-gray-100 px-1 rounded\"><span class=\"wp-katex-eq\" data-display=\"false\">\\sin(x)<\/span><\/code><\/li>\n            <li><code class=\"bg-gray-100 px-1 rounded\"><span class=\"wp-katex-eq\" data-display=\"false\">e^x<\/span><\/code><\/li>\n            <li><code class=\"bg-gray-100 px-1 rounded\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{1}{1-x}<\/span><\/code><\/li>\n            <li><code class=\"bg-gray-100 px-1 rounded\"><span class=\"wp-katex-eq\" data-display=\"false\">\\ln(1+x)<\/span><\/code><\/li>\n          <\/ul>\n        <\/div>\n      <\/div>\n    <\/div>\n\n    <div class=\"rounded-lg border border-gray-100 p-5 bg-white\">\n      <div class=\"flex items-start gap-3\">\n        <div class=\"flex-shrink-0 w-9 h-9 rounded-full bg-blue-600 text-white flex items-center justify-center font-bold\">2<\/div>\n        <div>\n          <h4 class=\"font-semibold text-gray-900 mb-1\">Select the Center Point<\/h4>\n          <p class=\"text-gray-600 text-sm\">\n            Choose the value of <span class=\"wp-katex-eq\" data-display=\"false\">a<\/span> in <span class=\"wp-katex-eq\" data-display=\"false\">(x - a)^n<\/span>.\n          <\/p>\n          <ul class=\"list-disc pl-5 mt-2 text-sm text-gray-700 space-y-1\">\n            <li>Most users choose <span class=\"wp-katex-eq\" data-display=\"false\">a = 0<\/span> for Maclaurin series<\/li>\n            <li>Other values create Taylor series around a specific point<\/li>\n          <\/ul>\n        <\/div>\n      <\/div>\n    <\/div>\n\n    <div class=\"rounded-lg border border-gray-100 p-5 bg-white\">\n      <div class=\"flex items-start gap-3\">\n        <div class=\"flex-shrink-0 w-9 h-9 rounded-full bg-blue-600 text-white flex items-center justify-center font-bold\">3<\/div>\n        <div>\n          <h4 class=\"font-semibold text-gray-900 mb-1\">Set the Order<\/h4>\n          <p class=\"text-gray-600 text-sm\">\n            Decide how many terms you want (e.g., 5, 8, or 10). More terms generally means higher accuracy.\n          <\/p>\n        <\/div>\n      <\/div>\n    <\/div>\n\n    <div class=\"rounded-lg border border-gray-100 p-5 bg-white\">\n      <div class=\"flex items-start gap-3\">\n        <div class=\"flex-shrink-0 w-9 h-9 rounded-full bg-blue-600 text-white flex items-center justify-center font-bold\">4<\/div>\n        <div>\n          <h4 class=\"font-semibold text-gray-900 mb-1\">Click Calculate<\/h4>\n          <p class=\"text-gray-600 text-sm\">Instantly receive:<\/p>\n          <ul class=\"list-disc pl-5 mt-2 text-sm text-gray-700 space-y-1\">\n            <li>The expanded power series<\/li>\n            <li>Each derivative step<\/li>\n            <li>Coefficient values<\/li>\n            <li>Final simplified result<\/li>\n          <\/ul>\n        <\/div>\n      <\/div>\n    <\/div>\n  <\/div>\n<\/div>\n\n<!-- Convergence -->\n<div id=\"convergence\" class=\"mb-10\">\n  <h3 class=\"text-xl font-semibold text-gray-900 mb-3\">\n    Understanding Radius and Interval of Convergence\n  <\/h3>\n\n  <div class=\"bg-yellow-50 border border-yellow-100 rounded-lg p-5\">\n    <p class=\"text-gray-700\">\n      Not every power series works for all values of <span class=\"wp-katex-eq\" data-display=\"false\">x<\/span>. A series may represent a function\n      only within a specific range.\n    <\/p>\n\n    <div class=\"mt-4 grid grid-cols-1 md:grid-cols-2 gap-4\">\n      <div class=\"bg-white rounded-lg border border-yellow-100 p-4\">\n        <h4 class=\"font-semibold text-gray-900 mb-2\">\n          Radius of Convergence <span class=\"wp-katex-eq\" data-display=\"false\">(R)<\/span>\n        <\/h4>\n        <p class=\"text-gray-700 text-sm mb-3\">\n          The radius of convergence tells you how far from the center <span class=\"wp-katex-eq\" data-display=\"false\">a<\/span> the series remains valid:\n        <\/p>\n        <pre class=\"bg-gray-900 text-gray-100 rounded-lg p-4 overflow-x-auto text-sm\"><code><span class=\"wp-katex-eq\" data-display=\"false\">|x - a| &lt; R<\/span><\/code><\/pre>\n        <p class=\"text-gray-600 text-sm mt-3\">\n          Inside this radius, the series converges. Outside it, the series diverges.\n        <\/p>\n      <\/div>\n\n      <div class=\"bg-white rounded-lg border border-yellow-100 p-4\">\n        <h4 class=\"font-semibold text-gray-900 mb-2\">\n          Interval of Convergence\n        <\/h4>\n        <p class=\"text-gray-700 text-sm mb-3\">\n          The interval of convergence includes all x-values where the series converges:\n        <\/p>\n        <pre class=\"bg-gray-900 text-gray-100 rounded-lg p-4 overflow-x-auto text-sm\"><code><span class=\"wp-katex-eq\" data-display=\"false\">(a - R, a + R)<\/span><\/code><\/pre>\n        <p class=\"text-gray-600 text-sm mt-3\">\n          Sometimes the endpoints are included\u2014sometimes not\u2014depending on the function.\n        <\/p>\n      <\/div>\n    <\/div>\n\n    <div class=\"mt-5\">\n      <h4 class=\"font-semibold text-gray-900 mb-2\">\n        Using the <a class=\"text-blue-600 hover:underline\" href=\"https:\/\/en.wikipedia.org\/wiki\/Ratio_test\" target=\"_blank\" rel=\"noopener noreferrer\">Ratio Test<\/a>\n      <\/h4>\n      <p class=\"text-gray-700 text-sm mb-3\">\n        The Ratio Test is commonly used to find convergence:\n      <\/p>\n      <pre class=\"bg-gray-900 text-gray-100 rounded-lg p-4 overflow-x-auto text-sm\"><code><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{n \\to \\infty} \\left| \\frac{a_{n+1}}{a_n} \\right|<\/span><\/code><\/pre>\n      <ul class=\"list-disc pl-5 mt-3 text-sm text-gray-700 space-y-1\">\n        <li>If result <span class=\"wp-katex-eq\" data-display=\"false\">&lt; 1<\/span> \u2192 converges<\/li>\n        <li>If result <span class=\"wp-katex-eq\" data-display=\"false\">&gt; 1<\/span> \u2192 diverges<\/li>\n        <li>If result <span class=\"wp-katex-eq\" data-display=\"false\">= 1<\/span> \u2192 inconclusive<\/li>\n      <\/ul>\n    <\/div>\n  <\/div>\n<\/div>\n\n<!-- Big 5 Series Table -->\n<div id=\"common-expansions\" class=\"mb-10\">\n  <h3 class=\"text-xl font-semibold text-gray-900 mb-3\">\n    Common Power Series Expansions (Maclaurin Series)\n  <\/h3>\n\n  <div class=\"overflow-x-auto rounded-lg border border-gray-100\">\n    <table class=\"min-w-full text-sm\">\n      <thead class=\"bg-gray-50\">\n        <tr>\n          <th class=\"text-left font-semibold text-gray-900 px-4 py-3\">Function<\/th>\n          <th class=\"text-left font-semibold text-gray-900 px-4 py-3\">Maclaurin Series<\/th>\n          <th class=\"text-left font-semibold text-gray-900 px-4 py-3\">Interval of Convergence<\/th>\n        <\/tr>\n      <\/thead>\n      <tbody class=\"bg-white divide-y divide-gray-100\">\n        <tr>\n          <td class=\"px-4 py-3\"><span class=\"wp-katex-eq\" data-display=\"false\">e^x<\/span><\/td>\n          <td class=\"px-4 py-3\"><span class=\"wp-katex-eq\" data-display=\"false\">\\sum_{n=0}^{\\infty} \\frac{x^n}{n!}<\/span><\/td>\n          <td class=\"px-4 py-3\"><span class=\"wp-katex-eq\" data-display=\"false\">(-\\infty, \\infty)<\/span><\/td>\n        <\/tr>\n        <tr>\n          <td class=\"px-4 py-3\"><span class=\"wp-katex-eq\" data-display=\"false\">\\sin(x)<\/span><\/td>\n          <td class=\"px-4 py-3\"><span class=\"wp-katex-eq\" data-display=\"false\">\\sum_{n=0}^{\\infty} \\frac{(-1)^n x^{2n+1}}{(2n+1)!}<\/span><\/td>\n          <td class=\"px-4 py-3\"><span class=\"wp-katex-eq\" data-display=\"false\">(-\\infty, \\infty)<\/span><\/td>\n        <\/tr>\n        <tr>\n          <td class=\"px-4 py-3\"><span class=\"wp-katex-eq\" data-display=\"false\">\\cos(x)<\/span><\/td>\n          <td class=\"px-4 py-3\"><span class=\"wp-katex-eq\" data-display=\"false\">\\sum_{n=0}^{\\infty} \\frac{(-1)^n x^{2n}}{(2n)!}<\/span><\/td>\n          <td class=\"px-4 py-3\"><span class=\"wp-katex-eq\" data-display=\"false\">(-\\infty, \\infty)<\/span><\/td>\n        <\/tr>\n        <tr>\n          <td class=\"px-4 py-3\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{1}{1-x}<\/span><\/td>\n          <td class=\"px-4 py-3\"><span class=\"wp-katex-eq\" data-display=\"false\">\\sum_{n=0}^{\\infty} x^n<\/span><\/td>\n          <td class=\"px-4 py-3\"><span class=\"wp-katex-eq\" data-display=\"false\">(-1, 1)<\/span><\/td>\n        <\/tr>\n        <tr>\n          <td class=\"px-4 py-3\"><span class=\"wp-katex-eq\" data-display=\"false\">\\ln(1+x)<\/span><\/td>\n          <td class=\"px-4 py-3\"><span class=\"wp-katex-eq\" data-display=\"false\">\\sum_{n=1}^{\\infty} \\frac{(-1)^{n-1} x^n}{n}<\/span><\/td>\n          <td class=\"px-4 py-3\"><span class=\"wp-katex-eq\" data-display=\"false\">(-1, 1]<\/span><\/td>\n        <\/tr>\n      <\/tbody>\n    <\/table>\n  <\/div>\n\n  <p class=\"text-gray-600 mt-3\">\n    These are often called the &#8220;Big 5&#8221; power series because many other expansions are built from them.\n  <\/p>\n<\/div>\n\n<!-- Worked example -->\n<div id=\"example\" class=\"mb-10\">\n  <h3 class=\"text-xl font-semibold text-gray-900 mb-3\">\n    Step-by-Step Example: Expansion of <span class=\"wp-katex-eq\" data-display=\"false\">\\frac{1}{1-x}<\/span>\n  <\/h3>\n\n  <div class=\"bg-blue-50 border border-blue-100 rounded-lg p-5\">\n    <div class=\"space-y-5 text-gray-700\">\n\n      <div>\n        <h4 class=\"font-semibold text-gray-900 mb-1\">Step 1: Recognize the Pattern<\/h4>\n        <p class=\"text-sm text-gray-700\">\n          The function <span class=\"wp-katex-eq\" data-display=\"false\">f(x)=\\frac{1}{1-x}<\/span> forms a geometric series.\n        <\/p>\n      <\/div>\n\n      <div>\n        <h4 class=\"font-semibold text-gray-900 mb-1\">Step 2: Evaluate at <span class=\"wp-katex-eq\" data-display=\"false\">x = 0<\/span><\/h4>\n        <pre class=\"bg-gray-900 text-gray-100 rounded-lg p-4 overflow-x-auto text-sm\"><code><span class=\"wp-katex-eq\" data-display=\"false\">f(0) = 1<\/span><\/code><\/pre>\n      <\/div>\n\n      <div>\n        <h4 class=\"font-semibold text-gray-900 mb-1\">Step 3: Take Derivatives<\/h4>\n        <div class=\"grid grid-cols-1 md:grid-cols-2 gap-3 text-sm\">\n          <pre class=\"bg-gray-900 text-gray-100 rounded-lg p-4 overflow-x-auto\"><code><span class=\"wp-katex-eq\" data-display=\"false\">f&#039;(x) = \\frac{1}{(1-x)^2}<\/span><\/code><\/pre>\n          <pre class=\"bg-gray-900 text-gray-100 rounded-lg p-4 overflow-x-auto\"><code><span class=\"wp-katex-eq\" data-display=\"false\">f&#039;&#039;(x) = \\frac{2}{(1-x)^3}<\/span><\/code><\/pre>\n          <pre class=\"bg-gray-900 text-gray-100 rounded-lg p-4 overflow-x-auto\"><code><span class=\"wp-katex-eq\" data-display=\"false\">f&#039;&#039;&#039;(x) = \\frac{6}{(1-x)^4}<\/span><\/code><\/pre>\n          <pre class=\"bg-gray-900 text-gray-100 rounded-lg p-4 overflow-x-auto\"><code>At <span class=\"wp-katex-eq\" data-display=\"false\">x=0<\/span>: <span class=\"wp-katex-eq\" data-display=\"false\">f(0)=1<\/span>, <span class=\"wp-katex-eq\" data-display=\"false\">f&#039;(0)=1<\/span>, <span class=\"wp-katex-eq\" data-display=\"false\">f&#039;&#039;(0)=2<\/span>, <span class=\"wp-katex-eq\" data-display=\"false\">f&#039;&#039;&#039;(0)=6<\/span><\/code><\/pre>\n        <\/div>\n      <\/div>\n\n      <div>\n        <h4 class=\"font-semibold text-gray-900 mb-1\">Step 4: Plug Into Taylor Formula<\/h4>\n        <pre class=\"bg-gray-900 text-gray-100 rounded-lg p-4 overflow-x-auto text-sm\"><code><span class=\"wp-katex-eq\" data-display=\"false\">f(x) = f(0) + f&#039;(0)x + \\frac{f&#039;&#039;(0)}{2!} x^2 + \\frac{f&#039;&#039;&#039;(0)}{3!} x^3 + \\cdots<\/span><\/code><\/pre>\n      <\/div>\n\n      <div>\n        <h4 class=\"font-semibold text-gray-900 mb-1\">Final Power Series<\/h4>\n        <pre class=\"bg-gray-900 text-gray-100 rounded-lg p-4 overflow-x-auto text-sm\"><code><span class=\"wp-katex-eq\" data-display=\"false\">1 + x + x^2 + x^3 + x^4 + \\cdots = \\sum_{n=0}^{\\infty} x^n<\/span><\/code><\/pre>\n      <\/div>\n\n      <div>\n        <h4 class=\"font-semibold text-gray-900 mb-1\">Step 5: Compare With Calculator Output<\/h4>\n        <p class=\"text-sm text-gray-700\">\n          A power series calculator instantly produces the same expansion, confirming the manual solution and saving time.\n        <\/p>\n      <\/div>\n\n    <\/div>\n  <\/div>\n<\/div>\n\n<!-- Why use -->\n<div id=\"why-use\" class=\"mb-10\">\n  <h3 class=\"text-xl font-semibold text-gray-900 mb-3\">\n    Why Use a Power Series Calculator with Steps?\n  <\/h3>\n\n  <div class=\"grid grid-cols-1 md:grid-cols-2 gap-4\">\n    <div class=\"bg-white rounded-lg border border-gray-100 p-5\">\n      <h4 class=\"font-semibold text-gray-900 mb-2\">Saves Time<\/h4>\n      <p class=\"text-gray-600 text-sm\">No need to compute endless derivatives manually.<\/p>\n    <\/div>\n    <div class=\"bg-white rounded-lg border border-gray-100 p-5\">\n      <h4 class=\"font-semibold text-gray-900 mb-2\">Reduces Mistakes<\/h4>\n      <p class=\"text-gray-600 text-sm\">Automatically applies formulas correctly.<\/p>\n    <\/div>\n    <div class=\"bg-white rounded-lg border border-gray-100 p-5\">\n      <h4 class=\"font-semibold text-gray-900 mb-2\">Improves Learning<\/h4>\n      <p class=\"text-gray-600 text-sm\">Shows each step clearly for deeper understanding.<\/p>\n    <\/div>\n    <div class=\"bg-white rounded-lg border border-gray-100 p-5\">\n      <h4 class=\"font-semibold text-gray-900 mb-2\">Handles Convergence<\/h4>\n      <p class=\"text-gray-600 text-sm\">Many tools include interval\/radius of convergence features.<\/p>\n    <\/div>\n  <\/div>\n\n  <div class=\"mt-6 bg-gray-50 border border-gray-100 rounded-lg p-5\">\n    <h4 class=\"font-semibold text-gray-900 mb-2\">Works for Complex Functions<\/h4>\n    <p class=\"text-gray-700 text-sm\">\n      Trigonometric, exponential, logarithmic, and rational functions become easier to expand and analyze using step-by-step output.\n    <\/p>\n  <\/div>\n<\/div>\n\n<!-- Final Thoughts -->\n<div id=\"final-thoughts\">\n  <h4 class=\"text-xl font-semibold text-gray-900 mb-3\">\n    Final Thoughts\n  <\/h4>\n  <div class=\"bg-green-50 border border-green-100 rounded-lg p-5\">\n    <p class=\"text-gray-700\">\n      A Power Series Calculator with Step-by-Step Solutions is more than just a shortcut\u2014it&#8217;s a learning companion.\n      By combining instant computation with clear explanations, it helps students master infinite series, understand\n      convergence behavior, and confidently solve advanced calculus problems.\n    <\/p>\n    <p class=\"text-gray-700 mt-3\">\n      With structured headings, educational depth, worked examples, and convergence theory, your page supports both\n      user satisfaction and strong content quality signals.\n    <\/p>\n  <\/div>\n<\/div>\n<div class=\"mb-6\" id=\"faqs\">\n  <h4 class=\"text-2xl font-semibold text-gray-900\">FAQs<\/h4>\n  <p class=\"text-gray-600 mt-2\">\n    Quick answers to common questions about Taylor\/Maclaurin series, convergence, and how to use a power series expansion effectively.\n  <\/p>\n<\/div>\n\n<div class=\"space-y-3\">\n\n  <details class=\"group bg-gray-50 border border-gray-100 rounded-lg p-4\">\n    <summary class=\"cursor-pointer list-none flex items-center justify-between gap-3\">\n      <span class=\"font-semibold text-gray-900\">\n        1. What is the difference between a Taylor Series and a Maclaurin Series?\n      <\/span>\n      <span class=\"text-blue-600 group-open:rotate-180 transition-transform duration-200\">\n        <i class=\"fas fa-chevron-down\"><\/i>\n      <\/span>\n    <\/summary>\n    <div class=\"mt-3 text-gray-700 text-sm\">\n      A Taylor Series is a power series expansion of a function about a specific point <span class=\"wp-katex-eq\" data-display=\"false\">a<\/span>.\n      A Maclaurin Series is simply a special case of the Taylor Series where the center point is <span class=\"wp-katex-eq\" data-display=\"false\">a = 0<\/span>.\n      Our power series calculator allows you to compute both by simply adjusting the center value.\n    <\/div>\n  <\/details>\n\n  <details class=\"group bg-gray-50 border border-gray-100 rounded-lg p-4\">\n    <summary class=\"cursor-pointer list-none flex items-center justify-between gap-3\">\n      <span class=\"font-semibold text-gray-900\">\n        2. How do you find the Radius of Convergence?\n      <\/span>\n      <span class=\"text-blue-600 group-open:rotate-180 transition-transform duration-200\">\n        <i class=\"fas fa-chevron-down\"><\/i>\n      <\/span>\n    <\/summary>\n    <div class=\"mt-3 text-gray-700 text-sm\">\n      The Radius of Convergence <span class=\"wp-katex-eq\" data-display=\"false\">(R)<\/span> defines the distance from the center <span class=\"wp-katex-eq\" data-display=\"false\">a<\/span>\n      within which the power series is guaranteed to converge. You can find it using the Ratio Test:\n      <pre class=\"bg-gray-900 text-gray-100 rounded-lg p-4 overflow-x-auto text-sm mt-3\"><code><span class=\"wp-katex-eq\" data-display=\"false\">L = \\lim_{n \\to \\infty} \\left| \\frac{a_{n+1}}{a_n} \\right|<\/span><\/code><\/pre>\n      <div class=\"mt-3\">\n        If <span class=\"wp-katex-eq\" data-display=\"false\">L &lt; 1<\/span>, the series converges. The radius is then\n        <span class=\"wp-katex-eq\" data-display=\"false\">R = \\frac{1}{L}<\/span>.\n        If the limit is <span class=\"wp-katex-eq\" data-display=\"false\">0<\/span>, the radius is infinity\n        <span class=\"wp-katex-eq\" data-display=\"false\">\\infty<\/span>.\n      <\/div>\n    <\/div>\n  <\/details>\n\n  <details class=\"group bg-gray-50 border border-gray-100 rounded-lg p-4\">\n    <summary class=\"cursor-pointer list-none flex items-center justify-between gap-3\">\n      <span class=\"font-semibold text-gray-900\">\n        3. Can a Power Series be differentiated or integrated?\n      <\/span>\n      <span class=\"text-blue-600 group-open:rotate-180 transition-transform duration-200\">\n        <i class=\"fas fa-chevron-down\"><\/i>\n      <\/span>\n    <\/summary>\n    <div class=\"mt-3 text-gray-700 text-sm\">\n      Yes! One of the biggest advantages of power series is that you can differentiate or integrate them term-by-term.\n      The resulting series will have the same radius of convergence as the original series, though the behavior at the\n      endpoints of the interval might change.\n    <\/div>\n  <\/details>\n\n  <details class=\"group bg-gray-50 border border-gray-100 rounded-lg p-4\">\n    <summary class=\"cursor-pointer list-none flex items-center justify-between gap-3\">\n      <span class=\"font-semibold text-gray-900\">\n        4. Why does my Power Series expansion only work for certain values of x?\n      <\/span>\n      <span class=\"text-blue-600 group-open:rotate-180 transition-transform duration-200\">\n        <i class=\"fas fa-chevron-down\"><\/i>\n      <\/span>\n    <\/summary>\n    <div class=\"mt-3 text-gray-700 text-sm\">\n      Because power series are approximations. The Interval of Convergence tells you exactly which values of\n      <span class=\"wp-katex-eq\" data-display=\"false\">x<\/span> make the series &#8220;behave&#8221; and equal the original function.\n      Outside of this interval, the series diverges, meaning the sum grows without bound and no longer represents the function accurately.\n    <\/div>\n  <\/details>\n\n  <details class=\"group bg-gray-50 border border-gray-100 rounded-lg p-4\">\n    <summary class=\"cursor-pointer list-none flex items-center justify-between gap-3\">\n      <span class=\"font-semibold text-gray-900\">\n        5. How many terms should I use in a Power Series expansion?\n      <\/span>\n      <span class=\"text-blue-600 group-open:rotate-180 transition-transform duration-200\">\n        <i class=\"fas fa-chevron-down\"><\/i>\n      <\/span>\n    <\/summary>\n    <div class=\"mt-3 text-gray-700 text-sm\">\n      The more terms you include, the more accurate your approximation becomes.\n      For most classroom problems, the first <span class=\"font-medium\">4 to 6 non-zero terms<\/span> are sufficient to show the pattern of the series.\n      Our calculator provides a customizable number of terms to fit your specific needs.\n    <\/div>\n  <\/details>\n\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":125,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"class_list":["post-59","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-series","infinite-scroll-item","generate-columns","tablet-grid-50","mobile-grid-100","grid-parent","grid-33"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Power Series Calculator | Expand Functions into Series<\/title>\n<meta name=\"description\" content=\"Power Series Calculator to find the nth-degree expansion of any function around a point. 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