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If `a_(1),a_(2),a_(3),"….",a_(n)` are in AP, where `a_(i)gt0` for all I, the value of `(1)/(sqrta_(1)+sqrta_(2))+(1)/(sqrta_(2)+sqrta_(3))+"....."+(1)/(sqrta_(n-1)+sqrta_(n))` is

A

`(sqrt(a_(1))+sqrta_(n))/(n)`

B

`(n)/(sqrt(a_(1))+sqrta_(n))`

C

`(n-1)/(sqrt(a_(1))+sqrta_(n))`

D

`n.sqrt((a_(1).a_(n)))`

Text Solution

Verified by Experts

The correct Answer is:
C
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