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Friday, 9 October

JEE Main 2022 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 25 July 2022, Shift 1, Maths Q27

Question 27 of 90 in this shift, Maths question 27 of 30, Section B.

If lim⁡n→∞(n+1)k−1nk+1[(nk+1)+(nk+2)+⋯+(nk+n)]=33⋅lim⁡n→∞1nk+1⋅[1k+2k+3k+⋯+nk]\lim_{n\to\infty}\frac{(n+1)^{k-1}}{n^{k+1}}\left[(nk+1)+(nk+2)+\dots+(nk+n)\right]=33\cdot\lim_{n\to\infty}\frac{1}{n^{k+1}}\cdot\left[1^k+2^k+3^k+\dots+n^k\right], then the integral value of kk is equal to ______.

Official answer

5

NTA final key (2022 Session 2).

Chapter
Integrals
Topic
Integral as Limit of Sum
Idea tested
Summation to Riemann Form

Same idea in other shifts

Asked 2× in all
  1. 9 Apr 2024, Shift 1 · Q28Let…HardNumerical value

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 42 of the 174 JEE Main shifts held from 2017 to 2026.