any help finding this limit: limit[n->infty] nth-root(n!) / n

[jk000jk]

I have the bellow limit, and I know I need to use Cauchy-d’Alembert, and the limit is 1/e but have no idea how to get to it, I get to something like \(\displaystyle \frac{\frac{\left(n+1\right)!}{n!}}{n}\), but is not right.

\(\displaystyle \lim _{n\to \infty }\left(\frac{\sqrt[n]{n!}}{n}\right)\)

 

[pka]

I have the bellow limit, and I know I need to use Cauchy-d’Alembert, and the limit is 1/e but have no idea how to get to it, I get to something like \(\displaystyle \frac{\frac{\left(n+1\right)!}{n!}}{n}\), but is not right.
\(\displaystyle \lim _{n\to \infty }\left(\frac{\sqrt[n]{n!}}{n}\right)\)

Do you have the theorem: \(\displaystyle \large{\left( {\dfrac{n}{{\sqrt[n]{n!}}}} \right) \to e}~?\)