Analysis: Prove divergence of sequence $(n!)^{\frac2n}$ I am trying to prove that the sequence $$a_n = (n!)^{\frac2n}$$ tends to infinity as $ n \to \infty $.
I've tried different methods but I haven't really got anywhere. Any solutions/hints?

Let $c_n=(n!)^2$; then $\displaystyle\frac{c_{n+1}}{c_n}=\frac{((n+1)!)^2}{(n!)^2}=(n+1)^2\to\infty,$ $\;\;\;$so $(n!)^{\frac{2}{n}}=(c_n)^{\frac{1}{n}}\to\infty$
