Published by:
CGP EDU Academic Team
Published on: August 11, 2026
A
tan –1 (n 2 + n + 1)
B
tan –1 (n 2 – n + 1)
C
tan –1 
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
C
tan –1 
= tan –1
⇒ tan –1 (m 2 + m + 1) – tan –1 (m 2 – m + 1)
So that 
= (tan –1 3 – tan –1 1) + (tan –1 7 – tan –1 3) + …. + tan –1 (n 2 + n +1) – tan –1 (n 2 – n + 1)
⇒ tan –1 (n 2 + n + 1) – tan –1 (1)
⇒ tan –1 
= (tan –1 3 – tan –1 ) + (tan –1 7 – tan –1 3) + …..+
(tan –1 (n 2 + n + 1) – tan –1 (n 2 – n + 1))
= tan –1 (n 2 + n + 1) – tan –1 (n 2 – n + 1)
= tan –1 
.
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