Regarding evaluation of the limit of the sequence $\Bigl(\frac{1}{n}\Bigr)^n+\Bigl(\frac{2}{n}\Bigr)^n+ \cdots \Bigl(\frac{n}{n}\Bigr)^n$
How to evaluate $ \lim \limits_{n\to \infty} \sum \limits_ {k=1}^n \frac{k^n}{n^n}$?