Question

Does the series converge or diverge? If it converges, find its sum:
Sum of (1/(n^3-n)) from 2 to infinity @Mathematics

Answer 1

I tried doing partial fractions and ended up with up\[\sum_{2}^{infinity}(-1/n +1/(2(n+1) + 1/(2(n-1))\]

I know the 1/n part diverges since it's a harmonic series. I also tried the integral test on the 2 other terms but they both tend to infinity. But Wolfram alpha says the sum converges to 1/4... I dunno how find it :(