A) \[\frac{3\pi }{4}-{{\cot }^{-1}}2\]
B) \[\frac{3\pi }{4}+{{\cot }^{-1}}2\]
C) \[\frac{\pi }{2}+{{\cot }^{-1}}3\]
D) \[\frac{\pi }{2}+ta{{n}^{-1}}2\]
Correct Answer: A
Solution :
[a] \[=\sum\limits_{n=1}^{\infty }{{{\tan }^{-1}}}\frac{(n+2)-(n-1)}{1+(n-1)\,\,(n+2)}\] \[={{\tan }^{-1}}0+{{\tan }^{-1}}1+{{\tan }^{-1}}2\] \[=\frac{\pi }{4}+{{\tan }^{-1}}2\] \[=\frac{\pi }{4}+\frac{\pi }{2}-{{\cot }^{-1}}2\] \[=\frac{3\pi }{4}-{{\cot }^{-1}}2\]You need to login to perform this action.
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