$\lim_{n\to \infty}\left(1 - \frac {1}{n^2}\right)^n =?$ Can you give any idea regarding the evaluation of the following limit? 
$\lim_{n\to \infty}\left(1 - \frac {1}{n^2}\right)^n$
We know that $\lim_{n\to \infty}\left(1 - \frac {1}{n}\right)^n = e^{-1}$, but how do I use that here?

Here is a hint:
$\left(1 - \dfrac{1}{n^2}\right) = \left(1 - \dfrac{1}{n}\right)\left(1 + \dfrac{1}{n}\right)$
Also use the fact that $(ab)^n = a^n b^n$.
