Limits of $n^{p/n}$ and $(n!)^{1/n}$ – math.stackexchange.com

Limits of $n^{p/n}$ and $(n!)^{1/n}$ – math.stackexchange.com

Determine the limits (i) $\lim_{n\rightarrow\infty}n^{p/n}$ where
$p\in\mathbb{R}$, and (ii) $\lim_{n\rightarrow\infty}(n!)^{1/n}.$ For (i),
I will prove that $\lim_{n\rightarrow\infty}n^{p/n}=1$ …