basic complex analysis (so z is complex):

Prove that the power series $\displaystyle $\sum_{k=0}^{\infty} z^{k}$$ converges at no point on its circle of convergence |z| = 1

Attempt:

I have no idea what to do. This course is driving me nuts. I know for |z| < 1 that series converges to 1/1-z but that is all I know. Can anyone give me a hint?