1+2015 = 2016

Calculus Level 5

\[\large{\displaystyle \sum^{\infty}_{n=1} \frac{1+2015^{n}}{2016^{n}n^{2}}=\frac{\pi^{A}}{B}+\ln (C) \ln(D)-(\ln(C))^2}\]

If the equation is true for positive integers \(A,B,C\) and \(D\), find \(A+B+C+D\).

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