Suppose that $\displaystyle f(z)=\sum_{n=0}^{\infty} c_nz^n$ for $\displaystyle z\in\mathbb{C}$. Prove that for all R, $\displaystyle \sum_{n=0}^{\infty}|c_n|R^n\leq2M(2R)$ where M(r):=sup{|f(z)|:|z|=r}.

I have absolutely no idea where to start with this question. Help starting would be much appreciated.