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∑n=2∞1(n2−1)n2=13⋅4+18⋅9+115⋅16+124⋅25+⋯ \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 n=2∑∞(n2−1)n21=3⋅41+8⋅91+15⋅161+24⋅251+⋯
The series above is equal to A−BπCD\dfrac{A-B\pi^{C}}{D}DA−BπC where A,B,CA,B,CA,B,C and DDD are positive integers with AAA and BBB coprime.
Find the value of A+B+C+DA+B+C+DA+B+C+D.
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