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, \(\displaystyle H_n^{(m)} = \sum_{k=1}^n \dfrac1{k^m} \).


Inspiration.

×

Problem Loading...

Note Loading...

Set Loading...