Sum of infinite non-geometric series: sum [n=20,infty] 40/(n^2-1)

[consolesvn]

Hello,

I have a question on how to solve the following problem: We are given a sum of 40/(n^2-1) where starting n=20 and it goes to infinity. We have to find the sum (I hope this is understandable). So my approach to solving this was using an integral from which I got Sn=20(ln|21|-ln|19|), which was not right as I later figured out that my result is actually less that what the sum of the series should equal to. I am now stuck on this step as I can't find other was to solve this problem. Any help would be greatly appriciated.

Thank you in advance.

 

[tkhunny]

Hello,

I have a question on how to solve the following problem: We are given a sum of 40/(n^2-1) where starting n=20 and it goes to infinity. We have to find the sum (I hope this is understandable). So my approach to solving this was using an integral from which I got Sn=20(ln|21|-ln|19|), which was not right as I later figured out that my result is actually less that what the sum of the series should equal to. I am now stuck on this step as I can't find other was to solve this problem. Any help would be greatly appriciated.

Thank you in advance.

Have you considered a Partial Fraction Decomposition and Telescoping?