JEE Math Practice Question
The sum of the infinite series $\cot ^{-1}\left(\frac{7}{4}\right)+\cot ^{-1}\left(\frac{19}{4}\right)+\cot ^{-1}\left(\frac{39}{4}\right)+\cot ^{-1}\left(\frac{67}{4}\right)+\ldots$. is :
- A.$\frac{\pi}{2}+\cot ^{-1}\left(\frac{1}{2}\right)$
- B.$\frac{\pi}{2}-\cot ^{-1}\left(\frac{1}{2}\right)$
- C.$\frac{\pi}{2}-\tan ^{-1}\left(\frac{1}{2}\right)$
- D.$\frac{\pi}{2}+\tan ^{-1}\left(\frac{1}{2}\right)$
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