$\lim_{n\to \infty}\left(1 - \frac {1}{n^2}\right)^n =?$ 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?

Hint: We can rewrite it as $\lim \limits_{n \to \infty} \left( (1 - \frac{1}{n^2} )^{n^2} \right)^{1/n}$
