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S(n) be the sum of n terms of the series...

`S_(n)` be the sum of n terms of the series `(8)/(5)+(16)/(65)+(24)/(325)+"......"`
The seveth term of the series is

A

`(56)/(2505)`

B

`(56)/(6505)`

C

`(56)/(5185)`

D

`(107)/(9605)`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `S_n=(8)/(5)+(16)/(65)+(24)/(325)+"......"`
`T_(r)=(8r)/(4r^(4)+1)=(8r)/((2^(2)+2r+1)(2^(2)-2r+1))`
`=2[((2^(2)+2r+1)-(2^(2)-2r+1))/((2^(2)+2r+1)(2^(2)-2r+1))]`
`=2[(1)/((2^(2)-2r+1))-(1)/((2^(2)+2r+1))]`
`T_(7)=(8xx7)/(4xx7^(2)+1)=(56)/(9605)`.
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