Geometric Series

A geometric series is the sum of a Geometric Sequence
where 'a' is called the first term and 'r' is called the ratio.

This will create the following geometric series where each successive term is obtained by multiplying the previous term by 1/2.

This series can be written as

Summing a Geometric Series

The sum of a geometric series is finite as long as the value of r is less than 1.
Despite the series containing an infinite number of terms they get smaller and smaller.
The sum of the first n terms when r is not equal to 1 is:

The sum of this series

would be

Summing a Geometric Series (to infinity)

The sum to infinity is: