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 \(b - a.\)
by
Brian Charlesworth