# How do you find the sum of the infinite geometric series 4/25+2/5+1+... ?

##### 1 Answer
Sep 1, 2016

The sum of this series does not converge.

#### Explanation:

A general term of this series is:

${a}_{n} = {\left(\frac{5}{2}\right)}^{n - 3} \text{ }$ $n = 1 , 2 , 3 , \ldots$

Since the common ratio $\frac{5}{2}$ is larger than $1$ the sum of this series does not converge. In fact it monotonically diverges to $+ \infty$.