The sum of the infinite series cot⁻¹(7/4)... | Inverse Trigonometric Functions

JEE MAIN 2025

4-4-2025 S2

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 :

Select the correct option:

$\frac{\pi}{2}-\tan ^{-1}\left(\frac{1}{2}\right)$

$\frac{\pi}{2}+\tan ^{-1}\left(\frac{1}{2}\right)$

$\frac{\pi}{2}+\cot ^{-1}\left(\frac{1}{2}\right)$

$\frac{\pi}{2}-\cot ^{-1}\left(\frac{1}{2}\right)$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Hard

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