Algebra
Intermediate

Infinite Geometric Series

Sum of an infinite geometric series that converges.

Formula

S=a11−r,∣r∣<1S = \frac{a_1}{1 - r}, \quad |r| < 1

Variables

a_1First term
rCommon ratio (

Example

1 + ½ + ¼ + ... = 2

Did You Know?

An infinite sum can add up to a finite number — Zeno's paradox of never reaching the wall is resolved by 1/2+1/4+1/8+··· = 1.

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