Analytic Function with a Pole at 1

[sbashrawi]

Homework Statement

Let r>1, let f be analytic in the disc (0,r)\{1}, and suppose that f has apole at 1.

Let sum(a(k) *z(k)) be the power series expansion of f in the disc (0,r). Prove that there is a positive integer N so that a(k) not equal to zero for k>= N, and that

lim (a(N+j+i)/a(N+1))=1

Homework Equations

The Attempt at a Solution

 

[sbashrawi]

no body replied on this problem

is it so hard?