- #1
nietzsche
- 186
- 0
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.