# Change in change in harmony

Calculus Level 4

$\large \sum_{n=1}^\infty \left [ H_n^{(2)} \left ( \dfrac1{n^2} - \dfrac1{(n+1)^2} \right) \right ]$

If the value of the series above is in the form of $$\dfrac{\pi^ A}B$$, where $$A$$ and $$B$$ are integers, find $$A+B$$.

Notation: $$H_n^{(m)}$$ denotes the generalized harmonic number, $$\displaystyle H_n^{(m)} = \sum_{k=1}^n \dfrac1{k^m}$$.