Find-the-sum-of-n-terms-1-1-3-1-3-5-1-2n-1-2n-1-

Question Number 45364 by Tawa1 last updated on 12/Oct/18

Find the sum of n terms : \frac{1}{1.3} + \frac{1}{3.5} + \dots + \frac{1}{(2 n - 1) (2 n + 1)} = ?

Answered by tanmay.chaudhury50@gmail.com last updated on 12/Oct/18

T_{n} = \frac{1}{(2 n + 1) (2 n - 1)}

T_{n} = \frac{1}{2} [\frac{(2 n + 1) - (2 n - 1)}{(2 n + 1) (2 n - 1)}]

T_{n} = \frac{1}{2} [\frac{1}{2 n - 1} - \frac{1}{2 n + 1}]

T_{1} = \frac{1}{2} [\frac{1}{1} - \frac{1}{3}]

T_{2} = \frac{1}{2} [\frac{1}{3} - \frac{1}{5}]

T_{3} = \frac{1}{2} [\frac{1}{5} - \frac{1}{7}]

\dots .

\dots

a d d t h e m

S_{n} = \frac{1}{2} [1 - \frac{1}{2 n + 1}]

Commented by Tawa1 last updated on 12/Oct/18

God bless you sir

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