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If \( a_{1}, a_{2}, a_{3}, a_{4}, \ldots a_{n} \) are \( n \) terms of an A.P. with common difference \( d \), then the value of the
P
expression
W
\[
\begin{array}{l}
\tan \left\{\tan ^{-1}\right.\left(\frac{d}{1+a_{1} a_{2}}\right)+\tan ^{-1}\left(\frac{d}{1+a_{2} a_{3}}\right) \\
\left.\quad+\tan ^{-1}\left(\frac{d}{1+a_{3} a_{4}}\right)+\ldots \tan ^{-1}\left(\frac{d}{1+a_{n-1} a_{n}}\right)\right\}
\end{array}
\]
(1) \( \frac{(n-1) d}{1+a_{1} a_{n}} \)
(2) \( \frac{(n+1) d}{1+a_{1} a_{n}} \)
(3) \( \frac{(n+1) d}{1-a_{1} a_{n}} \)
(4) \( \frac{(n-1) d}{1-a_{1} a_{n}} \)
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