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## Homework Statement

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

## The Attempt at a Solution

I think we should use the root test.

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

So the series is convergent.

Does it look alright?

Thanks in advance.