# How do you determine if #a_n=1+3/7+9/49+...+(3/7)^n+...# converge and find the sums when they exist?

##### 1 Answer

Convergent.

Sum to infinity

#### Explanation:

This is a geometric series:

The

Where:

If:

So we have:

Common ratio

First term is

The sum of a geometric series is given by:

From this we can see that if:

This is a finite value, and the sum is said to converge.

If:

The sum increases without bound, and is said to diverge.

We have