Question

A closed form for the sum $$ S = \frac {2}{3+1} + \frac {2^2}{3^2+1} + \cdots + \frac {2^{n+1}}{3^{2^n}+1} $$
is $1 - \frac{a^{n+b}}{3^{2^{n+c}}-1},$ where $a, b,$ and $c$ are integers. Find $a+b+c.$



Can someone help me? I have no idea how to do this problem. WILL MEDAL AND FAN.