How to prove that $\lim\limits_{n\to\infty} \frac{n!}{n^2}$ diverges to infinity? $\lim\limits_{n\to\infty} \dfrac{n!}{n^2} \rightarrow \lim\limits_{n\to\infty}\dfrac{\left(n-1\right)!}{n}$
I can understand that this will go to infinity because the numerator grows faster.  
I am trying to apply L'Hôpital's rule to this; however, have not been able to figure out how to take the derivative of $\left(n-1\right)!$ 
So how does one take the derivative of a factorial?  

By Stirling formula 
$$n!\sim\sqrt{2\pi n}\left(\frac{n}{e}\right)^n$$
the result that you look for is clear.
