🌪️ Sum of Geometric Series Calculator
Add up the terms of a finite geometric series, and see the infinite sum too when the ratio makes it converge.
What this calculator finds
A geometric series is the sum of the terms of a geometric sequence, where each term is the previous one multiplied by a fixed common ratio. This calculator finds the total of the first n terms, and, when the ratio’s absolute value is less than 1, the sum of the series continued forever.
The formula used
The sum of the first n terms is S_n = a1 × (1 – r^n) / (1 – r) when r is not 1. When the common ratio’s absolute value is less than 1, the series converges as n grows toward infinity, with an infinite sum of S = a1 / (1 – r). If |r| is 1 or greater, the series does not converge and has no finite infinite sum.
This tool is intended for general math learning and educational purposes.