Infinite Geometric Series Examples

Determine whether the infinite geometric series

converges or diverges. If it converges, find its sum.

Since r = 0.2 has magnitude less than 1, this series converges. The first term of the series is a = 5.

The sum of the series is

Determine whether the infinite geometric series

converges or diverges. If it converges, find its sum.

Since r = 2 has |r| ≥ 1, this series diverges. We don't have to find its sum, because its sum isn't defined.