hello all,.. I need help with this problem

Suppose that f is holomorphic in an open set containing the closed unit disc, except for a pole at z_0 on the unit circle. Show that if

\sum_{n=0}^{\infty} a_nz^n

denotes the power series expansion of f in the open unit disc, then

\lim_{n \to \infty} \frac{a_n}{a_{n+1}} = z_0.

I don't have any idea where should I start. thank for any comment and suggestion