Why is $\lim(n!)^{1/n}=\infty$ 
Why is $\lim\limits_{n\to\infty}(n!)^{1/n}=\infty$

It is more or less clear that the sequence is increasing by ratio test $\frac{((n+1)!)^{1/(n+1)}}{(n!)^{1/n}}=\frac{\sqrt[n+1]{(n+1)!}}{\sqrt[n+1]{(n)!}}\cdot\frac{\sqrt[n+1]{(n)!}}{\sqrt[n]{(n)!}}=\sqrt[n+1]{n+1}\cdot(n!)^{\frac{1}{n(n+1)}}$
but left multiplicand tends to $1$, what about the right one ? 
Is there convergence/divergence tests for sequences, I only found some for series ?

It is obvious that in calculating n!, you are multiplying at least n/2 numbers which are greater than n/2. 
$(n!)^{1/n} > ((n/2)^{n/2})^{1/n} = (n/2)^{1/2}$ which is clearly divergent. 
