question_answer

If \[{{a}_{1}},\]\[{{a}_{2}},\]\[{{a}_{3}},\]____., \[{{a}_{n}}\]is an A.P. with common difference d, then \[\tan \left[ {{\tan }^{-1}}\left( \frac{d}{1+{{a}_{1}}{{a}_{2}}} \right)+{{\tan }^{-1}}\left( \frac{d}{1+{{a}_{2}}{{a}_{3}}} \right)+.....+{{\tan }^{-1}}\left( \frac{d}{1+{{a}_{n-1}}{{a}_{n}}} \right) \right]=\]            

A)  \[\frac{(n-1)\,\,d}{{{a}_{1}}+{{a}_{2}}}\]                   

B)  \[\frac{(n-1)\,\,d}{1+{{a}_{1}}{{a}_{n}}}\] 

C) \[\frac{nd}{1+{{a}_{1}}{{a}_{n}}}\]              

D)  \[\frac{{{a}_{n}}-{{a}_{1}}}{{{a}_{n}}+{{a}_{1}}}\]                      

E)  None of these