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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

` sqrt(2n+1)-1`

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
d
Let `S_(n)= 1/(sqrt(1)+sqrt(3))+1/(sqrt(3)+sqrt(5))+...`
` = 1/2 [(sqrt(3)-1)+(sqrt(5)-1)+(sqrt(7)-sqrt(5))`
` + ...+ (sqrt(2n+1)-sqrt(2n-1))]`
` =1/2 (sqrt(2n+1)-1)`
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