Limits to infinity of a factorial function: $\lim_{n\to\infty}\frac{n!}{n^{n/2}}$ How can this limit to infinity be solved? I've tried with d'Alembert but it just keeps coming up with the wrong answer.
$$\lim\limits_{n\to\infty}\frac{n!}{n^{n/2}}$$
I might have a problem in simplifying factorial numbers. 
Thank you in advance. 

Hint:
use  Stirling's approximation:
$$n!\sim {\sqrt {2\pi n}}\left({\frac {n}{e}}\right)^{n}.$$
