Suppose that you can apply the Ratio Test to $\Sigma a_{n}$. Let $r$ be the limit of $|a_{n+1}|/|a_{n}|$. Show that $\lim\sup|a_{n}|^{1/n}=r$ as $n\rightarrow\infty$.
I know by definition of lim sup that $\forall\epsilon>0$, $\exists N_{\epsilon}$ s.t. $x_{n}