A product of our times

Calculus Level 3

\[\large \displaystyle\prod_{n=0}^{\infty} \left( 1 + \dfrac{1}{2015^{2^{n}}} \right) = \dfrac{a}{b}\]

For the equation above, given that \(a\) and \(b\) are positive coprime integers, find \(a + b.\)

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