Supported: +, -, *, /, ^ (power), sqrt(). Use 'n' as your index variable.
The total sum (Σ) is:
0
Understanding Summation Notation
Summation notation, also known as Sigma notation, is a convenient mathematical shorthand used to represent the sum of a sequence of numbers. The Greek capital letter Σ (Sigma) serves as the symbol for "sum."
Σ (expression) from n = lower to upper
This calculator allows you to input a variable expression and define the range of the index variable (n). It iterates through every integer from the lower limit to the upper limit, substitutes it into your expression, and adds all the results together.
How to Use This Calculator
Expression: Enter the mathematical formula you want to sum. Ensure you use "n" as your variable. For example, n^2 represents the sum of squares.
Lower Limit: The starting integer for the variable n.
Upper Limit: The ending integer for the variable n.
Common Summation Formulas
For quick reference, here are some standard formulas used in calculus and algebra:
Sum of first n integers: Σ n = [n(n + 1)] / 2
Sum of squares: Σ n² = [n(n + 1)(2n + 1)] / 6
Sum of cubes: Σ n³ = [n(n + 1) / 2]²
Example Calculation
If you want to find the sum of 2n + 1 where n goes from 1 to 3:
function calculateSummation() {
var exprInput = document.getElementById("expression").value;
var lower = parseInt(document.getElementById("lowerLimit").value);
var upper = parseInt(document.getElementById("upperLimit").value);
var resultBox = document.getElementById("sum-result-box");
var resultValue = document.getElementById("resultValue");
var stepDetails = document.getElementById("stepDetails");
if (isNaN(lower) || isNaN(upper)) {
alert("Please enter valid integers for the limits.");
return;
}
if (lower > upper) {
alert("The lower limit cannot be greater than the upper limit.");
return;
}
if ((upper – lower) > 10000) {
alert("To prevent browser lag, please choose a range smaller than 10,000 iterations.");
return;
}
// Clean expression to make it JS compatible
// Replace ^ with ** for power
var jsExpr = exprInput.replace(/\^/g, "**");
// Handle square root
jsExpr = jsExpr.replace(/sqrt\(/g, "Math.sqrt(");
var totalSum = 0;
var sequencePreview = [];
var isError = false;
try {
for (var n = lower; n <= upper; n++) {
// Use Function constructor instead of eval for slightly better safety/scope
// We create a function that takes 'n' as an argument
var evalResult = new Function('n', 'return ' + jsExpr)(n);
if (isNaN(evalResult) || !isFinite(evalResult)) {
throw new Error("Invalid calculation result");
}
totalSum += evalResult;
// Collect first few steps for preview
if (sequencePreview.length 4) {
stepsText += "…";
}
stepDetails.innerHTML = stepsText + "Iterated through " + (upper – lower + 1) + " steps.";
}
}