Summation notation (Σ, the Greek capital letter sigma) is a compact way to write "add up all these values." Instead of writing out a long string of additions, sigma notation names a formula and a range of index values, and the reader is expected to add the formula's output for every index in that range. This calculator evaluates any such summation for you, term by term.
How this calculator works
Enter an expression in terms of n — the index variable — along with a starting index (from) and ending index (to). The calculator plugs in every whole-number value of n in that range, evaluates the expression using a safe built-in parser (never a raw eval), and adds the results together. The Terms tab shows each individual value alongside a running total, so you can see exactly how the sum builds up term by term.
Inputs and what they mean
The expression accepts n, numbers, and the operators +, −, ×, ÷, ^ (exponent), and parentheses — including implicit multiplication like 2n or n(n+1). The "from" and "to" fields set the inclusive range of the index: a range of 1 to 10 evaluates 10 terms (n=1, 2, ..., 10). Ranges are capped at 100,000 terms to keep the calculation fast and the browser responsive.
Limits and edge cases
Only the variable n is supported — an expression using any other letter (like x or m) will return an error naming the unrecognized variable. If the expression divides by n and the range includes n=0 (or any other value that makes the denominator zero), the calculator stops and reports exactly which index caused the problem rather than silently skipping it. For summations with a known closed-form formula (like Σn or Σn²), the Formula Shortcuts tab lets you check the calculator's output against the textbook formula directly.