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. 

Consider:
$$n! = \int_0^\infty t^ne^{-t}\, dt > \int_n^{2n}t^ne^{-t}\, dt > n\cdot n^n e^{-2n} \ge n^ne^{-2n}.$$
Dividing by $n^{n/2}$ gives
$$ n!/n^{n/2} > n^{n/2}e^{-2n} = \exp [(n/2)\ln n - 2n].$$
Since $(n/2)\ln n - 2n \to \infty,$ the desired limit is $\infty.$ 
