A calculus problem by Vicky Vignesh

Calculus Level 5

\[\large \sum_{n=1}^\infty ~ \dfrac{1}{n^2- n - 1} \]

The series above can be expressed as \( \dfrac{\pi \tan\left(\frac{\sqrt A}B \pi \right)}{\sqrt A} \) for positive integers \(A\) and \(B\), find \(A+B\).

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