Convergence of Series: Using the Root Test to Prove Convergence

[nietzsche]

Homework Statement

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

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?

Thanks in advance.

 

[Mark44]

Looks fine.