I really got stuck with this question...guess it is not difficult, but i haven't done enough complex analysis...could anyone help me out? I am gonna take sub in 21, April!!!

If f is a function defined by a complex power series expansion in z-a which converges for |z-a|<1 and diverges for |z-a|>1, which of the following must be true?

A. f(z) is analytic in the open unit disk with center at a

B. The power series for f(z+a) converges for |z+a|<1

C. f'(a)=0

D. Integral f(z)dz over c=0 for any circle C in the plane

E. f(z) has a pole of order 1 at z=a

Answer: A

My thought is to apply the ratio test for convergence, and got lim f(n+1)/f(n)=1, but how can I get the answer and exclude other choices? Plzzzzzzzz help!