JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 28 June 2022, Shift 2, Maths Q18

Question 18 of 90 in this shift, Maths question 18 of 30, Section A.

The value of

\lim_{n\to\infty} 6\tan\left\{\sum_{r=1}^{n}\tan^{-1}\left(\frac{1}{r^2+3r+3}\right)\right\}

is equal to :

(1)1
(2)2
(3)3Official answer
(4)6

Official answer

Option 3

NTA final key.

Chapter: Inverse Trigonometric Functions
Topic: Inverse Trig Identities
Idea tested: Telescoping Inverse Trig Series

Same idea in other shifts

Asked 5× in all

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.