Just working through some practice problems before my final in a couple of weeks and I ran into one I couldn't figure out. Thanks!
Part A:
Let $ a_n = \gamma^{s/n} $ for some $ \gamma >1 $, some $ s>0$, and all positive integeers n. Show that $\lim_{n\to \infty} a_n = 1 $
Part B:
Fix some $s>0$. Determine (with proof!)
$ \lim_{n\to \infty} {\gamma^{s/n}-1\over\gamma^{1/n}-1} $