Limit of a Sequence (limit at infinity)

Question

Who can help me to find the following limit?
$\lim _{n\to \infty}\frac{e^n\times n!}{n^n}=?$

Answer 1

Use the Stirling formula:

$\displaystyle n!\simeq \sqrt{2\pi n}\left({n\over e}\right)^n$ implies that $\displaystyle\lim_{n\rightarrow +\infty}{{e^nn!}\over n^n}=\lim_{n\rightarrow +\infty}\sqrt{2\pi n}=+\infty.$

https://en.wikipedia.org/wiki/Stirling%27s_approximation