It's an exercise in Luarent Series.How to prove it?

f(Z)=1/z+\(\displaystyle sum_{n=1}^{infinity}a_{n}z^n\) is univalent and holomorphic in domain B(0,1)\{1}. Prove that

\(\displaystyle sum_{n=1}^{infinity}n\left|a_{n}\right|^2\) <=1

Is it called Area Theorem?