n-0-1-n-2-1-

Question Number 99894 by bachamohamed last updated on 23/Jun/20

\sum_{n ⩾ 0} \frac{1}{n^{2} + 1} = ?

Answered by smridha last updated on 24/Jun/20

s (a) = \underset{n = 1}{\sum^{\infty}} \frac{1}{n^{2} + a^{2}} = \frac{π c o t h (π a)}{2 a} - \frac{1}{2 a^{2}}

n o w s (1) = \frac{π c o t h (π)}{2} - \frac{1}{2} \approx 1.0766 \dots

n o w \underset{n = 0}{\sum^{\infty}} \frac{1}{n^{2} + 1} = 1 + \underset{n = 1}{\sum^{\infty}} \frac{1}{n^{2} + 1} \approx 2.0766 \dots .

Facebook Tweet Pin