show $\sum_{n=0}^{\infty}{z^n\over n}$ is convergent on the unit circle

Question

I need to show $\sum_{n=0}^{\infty}{z^n\over n}$ is convergent on the unit circle except the point $z=1$, well at $z=1$ we get our known divergent harmonic series, but I am not able to show easily the other part.