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The sum of n terms of the series 1/(sqrt...

The sum of `n` terms of the series `1/(sqrt1+sqrt3)+1/(sqrt3+sqrt5)+...` is

A

`sqrt(2n+1)`

B

`(1)/(2)sqrt(2n+1)`

C

`sqrt(2n+1)-1`

D

`(1)/(2)(sqrt(2n+1)-1)`

Text Solution

Verified by Experts

The correct Answer is:
D
The required sum to n terms is given by
`(1)/(sqrt(1)+sqrt(3))+(1)/(sqrt(3)+sqrt(5))+(1)/(sqrt(5)+sqrt(7))+ . . .+(1)/(sqrt(2n-1)+sqrt(2n+1))`
`=(1)/(2)[(sqrt(3)-sqrt(1))+(sqrt(5)-sqrt(3))+(sqrt(7)-sqrt(5))+(sqrt(2n+1)-sqrt(2n-1))]`
`=(1)/(2)(sqrt(2n+1)-1)`
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