# Complex power series question

Find radius of convergence of $f(z) = \sum \frac{z^n}{2^n+1}$ and prove that $(2-z)f(z) - 2 \rightarrow 0$ as $z \rightarrow 2$.
The first part I can get the radius of convergence as $|z| \leq 2$. How do I do the 2nd part?