question_answer

\[\sum\limits_{m=1}^{n}{{{\tan }^{-1}}\left( \frac{2m}{{{m}^{4}}+{{m}^{2}}+2} \right)}\]is equal to

A) \[{{\tan }^{-1}}\left( \frac{{{n}^{2}}+n}{{{n}^{2}}+n+2} \right)\]   

B) \[{{\tan }^{-1}}\left( \frac{{{n}^{2}}-n}{{{n}^{2}}-n+2} \right)\]

C) \[{{\tan }^{-1}}\left( \frac{{{n}^{2}}+n+2}{{{n}^{2}}+n} \right)\]   

D)  All of these

E)  None of these