# Convergence of series

1. Mar 28, 2010

### nietzsche

1. The problem statement, all variables and given/known data

$$\text{Show that }\sum_{n=1}^{\infty} \left( \frac{e}{n} \right) ^n \text{converges.}$$

3. The attempt at a solution

I think we should use the root test.

$$\lim_{n \to \infty} \sqrt[n]{\left( \frac{e}{n} \right) ^n} = \lim_{n \to \infty} \frac{e}{n} = 0 < 1$$

So the series is convergent.

Does it look alright?