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 $a+b+c.$
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