S-n-0-n-2-n-1-n-3-does-S-converge-

Question Number 2497 by 123456 last updated on 21/Nov/15

S = \underset{n = 0}{\sum^{+ \infty}} \frac{n + 2}{(n + 1) (n + 3)}

does S converge ?

Answered by prakash jain last updated on 21/Nov/15

S = \underset{n = 0}{\sum^{\infty}} \frac{n + 2}{(n + 1) (n + 3)} = \frac{1}{2} \underset{n = 0}{\sum^{\infty}} [\frac{1}{n + 1} + \frac{1}{n + 3}]

S diverges as \frac{1}{n} does not converge .