This question seems like it should be so easy, but I just can't quite get there:

Use the fact that $\displaystyle (1 + \frac{1}{n})^n \rightarrow e$ to deduce that $\displaystyle (1 - \frac{1}{n})^n \rightarrow \frac{1}{e}$.

So far this is what I have but I have a feeling i'm going about it the wrong way:

$\displaystyle (\frac{n+1}{n})^n \rightarrow e$

By algebra of limits: $\displaystyle (\frac{n}{n+1})^n \rightarrow \frac{1}{e}$

So $\displaystyle (1- \frac{1}{n+1})^n \rightarrow \frac{1}{e}$.

But from here I can't see how I can get the answer required.