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.

Since
$$n!=1\cdot 2\cdot 3\cdot 4\cdot 5\cdot \cdots \cdot n\ge 2\cdot 3\cdot 4^{n-3}$$
$$\frac{n!}{n\cdot 2^n} \ge 2\cdot 3\cdot \frac{4^{n-4}}{2^n}=\frac{2\cdot3}{4^4} 2^n$$
for $n\ge 4$. Therefore the sequence diverges.
