JEE Main 2021 · 24 Feb · Shift 1 · Mathematics Q90

MathematicsInteger+4 / -1Question 90 of 90

$\displaystyle\lim_{n\to\infty}\tan\left\{\sum_{r=1}^n\tan^{-1}\left(\frac1{1+r+r^2}\right)\right\}$ is equal to _______.

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Answer and worked solution

Official answer: 1

Telescope. $\tan^{-1}\frac1{1+r(r+1)}=\tan^{-1}(r+1)-\tan^{-1}r$ , so the sum tends to $\frac\pi2-\frac\pi4=\frac\pi4$ , whose tangent is 1.

Answer: 1

JEE Main 2021 · 24 Feb · Shift 1, Mathematics question 90