How to find the above summation upto infinity?

Asked Jul 23 '23 at 09:08

Active Jul 23 '23 at 09:24

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How to find the summation of this series upto infinity?

$$\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+\cdots\infty$$

Actually I know how to find the summation of a telescopic sequence like $\frac{1}{(1×2)}+\frac{1}{(2×3)}+\frac{1}{(3×4)},...$ upto $\infty$. But how to find the summation of the above series upto infinity? As far as I know the above series is not a telescopic series.

edited Jul 23 '23 at 09:23

NadiKeUssPar

2,474

asked Jul 23 '23 at 09:08

Syamaprasad Chakrabarti

1,269

Welcome to MSE. It is in your best interest that you type your posts (using MathJax) instead of posting links to pictures. – José Carlos Santos Jul 23 '23 at 09:11
But how to proceed after that? – Syamaprasad Chakrabarti Jul 23 '23 at 09:15
I don't think that the above series is a telescopic series – Syamaprasad Chakrabarti Jul 23 '23 at 09:15
Thanks for helping. – Syamaprasad Chakrabarti Jul 23 '23 at 09:21

How to find the above summation upto infinity?

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