Psi and Riemann together?

Calculus Level 5

\[\sum _{ k=1 }^{ \infty }{ \dfrac { { \psi }^{ 1 }\left( k \right) }{ k } } =\sum _{ n=1 }^{ \infty }{ \dfrac { A }{ { n }^{ B } } } \]

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


Inspired by Ishan.
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