How I show that
For a large n,
See here : http://en.wikipedia.org/wiki/Stirling%27s_approximation
you already asked this and i already gave you a hint. not very polite of you to re-post Andres.
we don't have a series here, we have a limit. doing the ratio test was a beat around the bush way to attack this problem. of course, it yields no fruit since the limit was exactly 1, it gives us no information.How we show the divergence of the series?
a variation on the root test may work though.