How to use the Series (Sigma) Calculator
- Choose a sigma sum or an infinite geometric series.
- Type the expression in n and the limits — or the first term and ratio.
- Read the total and the running sums.
What does this tool do?
Sigma notation Σ is shorthand for adding many terms that follow a rule. Σ n² from 1 to 10 means 1 + 4 + 9 + … + 100 = 385.
An infinite geometric series a + ar + ar² + … converges to a ÷ (1 − r) when −1 < r < 1. For example 1 + ½ + ¼ + … = 2.
Why use it?
- Any expression, not just preset series.
- Up to a million terms, summed carefully to avoid rounding drift.
- Running totals to see convergence.
The formula
Σ from n = a to b of f(n)
Infinite geometric: S = a ÷ (1 − r), |r| < 1
Privacy
The calculation happens instantly in your browser. The numbers you enter are not sent to our servers or saved. There's no account to create and nothing to install.
Frequently asked questions
Can it tell if an infinite series converges?
Only geometric series are summed to infinity. For other series, sum a large number of terms and watch whether the running total settles.
Last reviewed by the M2Toolkit team.