Jeeify
MCQMediumJEE Main 2025 · 4 April, Shift 2Sum of Series

Mathematics Question from JEE Main 2025 · 4 April, Shift 2

The sum of the infinite series cot⁡−1(74)+cot⁡−1(194)+cot⁡−1(394)+cot⁡−1(674)+…\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) + \dots is:

  • A

    π2+tan⁡−1(12)\frac{\pi}{2} + \tan^{-1} \left( \frac{1}{2} \right)

  • B

    π2−cot⁡−1(12)\frac{\pi}{2} - \cot^{-1} \left( \frac{1}{2} \right)

  • C

    π2+cot⁡−1(12)\frac{\pi}{2} + \cot^{-1} \left( \frac{1}{2} \right)

  • D

    π2−tan⁡−1(12)\frac{\pi}{2} - \tan^{-1} \left( \frac{1}{2} \right)

Answer & step-by-step solution

Sign in to reveal the correct answer, the full step-by-step solution, and the common mistakes for this question.

Sign in to see the solution

Practice more Sum of Series questions

Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step - free to start.

Start free trialMore on Sum of Series

Related questions