Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Find the sum of n terms of the series cot –1 (2. 1 2 ) + cot –1 (2.2 2 ) + cot –1 (2.3 2 ) +……. and hence find the sum of infinite terms.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
The r th term of the given series is
T r = cot –1 (2r 2 )
= tan –1 
= tan –1 
= tan –1 
= tan –1 
T r = tan –1 (2r +1) – tan –1 (2r –1) …(1)
Put r = 1, 2, 3,……n in (1) and add then
S n = tan –1 (2n+ 1) – tan –1 1
∴ S ∞ = tan –1 ( ∞ ) – π /4
= 
– 
= 
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems