# 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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