# Tricky Sum!

Algebra Level 4

$\sum_{n=2}^\infty \dfrac1{(n^2-1)n^2} = \dfrac{1}{3\cdot4}+\dfrac{1}{8\cdot 9}+\dfrac{1}{15\cdot16}+\dfrac{1}{24\cdot25}+\cdots$

The series above is equal to $$\dfrac{A-B\pi^{C}}{D}$$ where $$A,B,C$$ and $$D$$ are positive integers with $$A$$ and $$B$$ coprime.

Find the value of $$A+B+C+D$$.

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