# An unusual sum

Calculus Level 4

$\large{\displaystyle \sum _{ r=1 }^{ 2014 }{ \psi \left( \frac { r }{ 2015 } \right) \sin { \left( \frac { 2\pi r }{ 2015 } \right) } } =-\frac{A}{B}\pi}$

Given that the summation above is equal to $$-\dfrac AB \pi$$, where $$A$$ and $$B$$ are coprime positive integers, and $$\psi (x)$$ denote the digamma function. Find the value of $$A+B$$,

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