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

There is yet another approach that I found today:
For a sequence $(a_{n})$ of positive terms, we have
$$\liminf_{n\rightarrow \infty}\frac{a_{n+1}}{a_{n}}\leq \liminf_{n\rightarrow \infty}(a_{n})^{1/n}\leq \limsup_{n\rightarrow \infty} (a_{n})^{1/n}\limsup_{n\rightarrow \infty}\frac{a_{n+1}}{a_{n}}$$
This immediately implies the result as $\lim\limits_{n\rightarrow \infty} \frac{(n+1)!}{n!} = \infty$
