Find the sum `Sigma_(r=1)^(oo)(3n^2+1)/((n^2-1)^3)` – InterviewSolution

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1.	Find the sum `Sigma_(r=1)^(oo)(3n^2+1)/((n^2-1)^3)`
Answer» Correct Answer - `9/16` `T_(n)=(3n^(2)+1)/((n^(2)-1)^(3))=1/2(6n^(2)+2)/((n^(2)-1)^(3))` `=1/2(((n+1)^(3)-(n-1)^(3))/((n+1)^(3)(n-1)^(3)))` `=1/2(1/((n-1)^(3))-1/(n+1)^(3))` `thereforeS=1/2[(1/1^(3)-1/3^(3))+(1/2^(3)-1/3^(3))+(1/2^(3)-1/4^(3))+(1/3^(3)-1/5^(3))` `+(1/4^(3)-1/6^(3))+...]` `=1/2(1+1/8)=9/16`

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