Infinite Geometric Series

http://www.intmath.com/series-binomial-theorem/3-infinite-geometric-series.php

If −1<r<1, then the infinite geometric series

a₁ + a₁r + a₁r² + a₁r³ + ... + a₁r^n-1

converges to a particular value.
This value is given by:

S∞=a11−r (|r|<1)

The series converges because each term gets smaller and smaller (since -1 < r < 1).