# Partial fraction challenge

Algebra Level 4

$S=\frac{1}{4(1)^{4}+1}+\frac{2}{4(2)^{4}+1}+\frac{3}{4(3)^{4}+1}+\dots+\frac{2016}{4(2016)^{4}+1}$

If the sum above $$S = \dfrac{2017p}{2017q+1}$$, where $$p$$ and $$q$$ are positive integers, find $$p+q$$.

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