How to solve : $\lim_{n\rightarrow \infty} \frac{n!}{n\cdot 2^{n}}$ $$\lim_{n\rightarrow \infty} \frac{n!}{n\cdot 2^{n}}$$
I need to solve the limit problem above. I have no idea about what to do. What do you suggest?
Thanks in advance.

Use Stirling's formula $n!=\sqrt{2\pi n}\left(\frac{n}{e}\right)^n(1+O(\frac{1}{n}))$. You wil get
$\frac{n!}{n2^n}=\sqrt{\frac{2\pi}{n}}\left(\frac{n}{2e}\right)^n(1+O(\frac{1}{n}))\to  \infty$
