If \( a_{1}, a_{2}, a_{3}, \ldots \ldots \ldots \). an is an A.P. with common difference \( d \)...
If \( a_{1}, a_{2}, a_{3}, \ldots \ldots \ldots \). an is an A.P. with common difference \( d \) then
\( \tan \left[\tan ^{-1}\left(\frac{d}{1+a_{1} a_{2}}\right)+\tan ^{-1}\left(\frac{d}{1+a_{2} a_{3}}\right)+\ldots \ldots\right. \)
\( \left.+\tan ^{-1}\left(\frac{d}{1+a_{n-1} a_{n}}\right)\right] \) is equal to:
(a) \( \frac{(n-1) d}{a_{1}+a_{n}} \)
(b) \( \frac{(n-1) d}{1+a_{1} a_{n}} \)
(c) \( \frac{n d}{1+a_{1} a_{n}} \)
(d) \( \frac{a_{n}-a_{1}}{a_{n}+a_{1}} \)
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