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If a(1),a(2),a(3),...a(n) are in A.P. wi...

If `a_(1),a_(2),a_(3),...a_(n)` are in A.P. with common difference d, then `tan[tan^(-1)((d)/(1+a_(1)a_(2)))+tan^(-1)((d)/(1+a_(2)a_(3)))+,....+tan^(-1)((d)/(1+a_(n-1)a_(n)))]=`

A

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

B

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

C

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

D

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

Text Solution

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The correct Answer is:
B
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