Who's up to the challenge? 30

Calculus Level 5

\[ \large \displaystyle\sum _{ n=2 }^{ \infty }{ \dfrac { 1 }{ { n }^{ 4 }-{ n }^{ 3 } } } =\dfrac { { \psi }^{ (H) }(U) }{ M } +{ M }_{ 1 }-\frac { { \pi }^{ { U }_{ 1 } } }{ S } \]

The equation above holds true for positive integers
\(H,U,M,M_1,U_1\) and \( S\). Find \(H+U+M+M_1+U_1+S\).

Notation: \(\psi^{(n)}(\cdot)\) denotes the \(n^\text{th}\) derivative of the Digamma function.


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