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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