# Convergence of a series

1. Nov 3, 2009

### ganondorf29

1. The problem statement, all variables and given/known data
Find the radius of convergence and the interval of convergence for
$$\sum_{n=0}^\infty \frac{x^n}{n3^n}$$

2. Relevant equations

3. The attempt at a solution
Ok, so I first applied the ratio test.
$$\lim_{n\rightarrow\infty} | \frac{x^{n+1}}{(n+1)3^(n+1)} / \frac{x^n}{n3^n} |$$

After some cancellations I got

$$L = |x/3|$$

Does this mean that the interval of convergence is from -3<x<3 ?

2. Nov 3, 2009

Yes.

3. Nov 4, 2009

### Office_Shredder

Staff Emeritus
You have to check the endpoints of your interval separately to see if the series converges there since the ratio test doesn't give any information when the limit is 1