Given that $\displaystyle (1+1/n)^n \rightarrow e$ as $\displaystyle n \rightarrow \infty$, show that $\displaystyle (1+1/n)^{n+1} \rightarrow e$ as $\displaystyle n \rightarrow \infty$. Note: May use theorems containing sums, products, or quotients of convergent sequences.