$\lim\limits_{n \to{+}\infty}{\sqrt[n]{n!}}$ is infinite How do I prove that $ \displaystyle\lim_{n \to{+}\infty}{\sqrt[n]{n!}}$ is infinite?

Using $\text{AM} \ge \text{GM}$
$$ \frac{1 + \frac{1}{2} + \dots + \frac{1}{n}}{n} \ge \sqrt[n]{\frac{1}{n!}}$$
$$\sqrt[n]{n!} \ge \frac{n}{H_n}$$
where $H_n = 1 + \frac{1}{2} + \dots + \frac{1}{n} \le \log n+1$
Thus
$$\sqrt[n]{n!} \ge \frac{n}{\log n+1}$$
