# lim\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?

$n! \geq (n/2)^{n/2}$ because half of the factors are at least $n/2$. Take $n$-th root.