# Convergence of a series

## Homework Statement

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

## 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 ?

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Dick