# Tricky 2015 Sum

Calculus Level 3

$\displaystyle\sum_{n=0}^{\infty} \dfrac{1}{2015^{2^{n}} - 2015^{-(2^{n})}}$

If the closed form of the series above is in the form $$\frac a b$$, where $$a$$ and $$b$$ are positive coprime integers, then find $$b - a.$$

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