# Summation Contest Conceptual Problem On Digamma Function

Calculus Level 5

$\sum _{ n=1 }^{ \infty }{ \frac { 1 }{ { n }^{ 2 }+4 } } =\frac { \pi }{ A } \coth { \left( B\pi \right) } -\frac { 1 }{ C }$

The above equation holds true for positive integers $$A$$, $$B$$ and $$C$$. Find $$A+B+C$$.

Hint: Exploit partial fractions and relate it to the digamma function.

×