Here's a question that really makes me confused and I don't even know how to start solving it.
Let $\sum a_n(z-a)^n$ define a Laurent series expansion that converges uniformly to a function $f$ in the disk $D(a,r),r>0$. Show that: $$\sum\vert a_n \vert^2 r^{2n} = \frac{1}{2 \pi} \int_0^{2 \pi} \vert f(a+r e^{i \theta}) \vert ^2 d\theta <[M(r)]^2$$
such that $M(r)=sup_{z \in D(a,r)} \vert f(z) \vert$
How can I start solving the problem?