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If a(1),a(2),a(3), . . .,a(n) are in AP...

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

A

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

B

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

C

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

D

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

Text Solution

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The correct Answer is:
D
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