What is the Interval of Convergence for the Series x^n/(n3^n)?

[ganondorf29]

Homework Statement

Find the radius of convergence and the interval of convergence for
$$\sum_{n=0}^\infty \frac{x^n}{n3^n}<br />$$

Homework Equations

The Attempt at a Solution

Ok, so I first applied the ratio test.
$$\lim_{n\rightarrow\infty}<br /> <br /> |<br /> \frac{x^{n+1}}{(n+1)3^(n+1)} /<br /> \frac{x^n}{n3^n}<br /> |$$

After some cancellations I got

$$L = |x/3|<br />$$Does this mean that the interval of convergence is from -3<x<3 ?

 

[Dick]

Yes.

 

[Office_Shredder]

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