The sum of the infinite series \cot ^{-1} (\frac{7}{4}) +\cot ^{-1} (\frac{19}{4}) +\cot ^{-1} (\frac{39}{4}) +\cot ^{-1} \frac{67}{4}+. . . is: [4 Apr 2025 Shift 2]

Correct Answer is : π2−tan−1(12)

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

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

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

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

JEE Main 4 Apr 2025 Shift 2 Paper

Section: Mathematics

Question : 20 of 75

Marks: +1, -0

The sum of the infinite series cot−1(‌

)+cot−1(‌

)+cot−1‌

+... is:

[4 Apr 2025 Shift 2]

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