n-2-2-n-2-1-

Question Number 123067 by Khalmohmmad last updated on 22/Nov/20

\underset{n = 2}{\sum^{\infty}} \frac{2}{n^{2} - 1} = ?

Answered by Dwaipayan Shikari last updated on 22/Nov/20

2 \underset{n = 2}{\sum^{\infty}} \frac{1}{n^{2} - 1} = \sum^{\infty} \frac{1}{n - 1} - \sum^{\infty} \frac{1}{n + 1} = (1 + \frac{1}{2} + \frac{1}{3} + . .) - (\frac{1}{3} + \frac{1}{4} + . .) = 1 + \frac{1}{2}

= \frac{3}{2}