Algebra
Advanced

Infinite Geometric Series

Sum of an infinite geometric series that converges.

Formula

S=a1−r,  ∣r∣<1S = \frac{a}{1-r}, \; |r|<1

Variables

aFirst term
rCommon ratio

Example

1+½+¼+... = 2

Did You Know?

An infinite series of shrinking terms can add up to a finite total — the resolution of Zeno's ancient paradoxes.

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