Question

show lim (n!)^(1/n) = infinity

Answer 1

@Hero @ganeshie8 @iambatman

Answer 2

you may use stirling's approximaiton
http://en.wikipedia.org/wiki/Stirling's_approximation

Answer 3

how about showing lim r^n/n! = 0

Answer 4

You may use the fact that below series converges to \(e^r\) :
\[\sum\limits_{n=0}^{\infty}\dfrac{r^n}{n!}=e^r\]

Since the series converges, the corresponding sequence must converge to 0 :
\[\lim\limits_{n\to\infty} \dfrac{r^n}{n!}=0\]