If \[{{a}_{1}},{{a}_{2}},{{a}_{3}},....{{a}_{n}}\] is an \[A.P.\] with common difference d; \[(d>0)\] then \[\tan \left[ {{\tan }^{-1}}\left( \frac{d}{1+{{a}_{1}}{{a}_{2}}} \right)+{{\tan }^{-1}}\left( \frac{d}{1+{{a}_{2}}{{a}_{3}}} \right)+...+ta{{n}^{-1}}\left( \frac{d}{1+{{a}_{n-1}}{{a}_{n}}} \right) \right]\]is equal to

• A. \[\frac{(n-1)d}{{{a}_{1}}+{{a}_{n}}}\]
• B. \[\frac{(n-1)d}{1+{{a}_{1}}{{a}_{n}}}\]
• C. \[\frac{nd}{1+{{a}_{1}}{{a}_{n}}}\]
• D. \[\frac{{{a}_{n}}-{{a}_{1}}}{{{a}_{n}}+{{a}_{1}}}\]