# Change in Harmony

Calculus Level 5

$\sum _{ n=1 }^{ \infty }{ \dfrac { { H }_{ n }^{ \left( 2 \right) } }{ { \left( n+1 \right) }^{ 2 } } } =\dfrac { { \pi }^{ A } }{ B }$

If the equation above holds true for positive integers $$A$$ and $$B$$, find $$A+B.$$

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

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