For $\displaystyle | z | \neq 1 $, show that the following limit exists:

$\displaystyle f(z) = \lim _{n \rightarrow \infty } \frac {z^n -1 }{z^n + 1 } $

How to define $\displaystyle f(z) $ when $\displaystyle |z| = 1 $ in such a way to make f continuous?

Thanks.