JEE Main 2022 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 29 July 2022, Shift 1, Maths Q28

Question 28 of 90 in this shift, Maths question 28 of 30, Section B.

\frac{1}{2 \times 3 \times 4} + \frac{1}{3 \times 4 \times 5} + \frac{1}{4 \times 5 \times 6} + \ldots + \frac{1}{100 \times 101 \times 102} = \frac{k}{101}

, then

34k

is equal to __________.

Official answer

286

NTA final key.

Chapter: Sequences and Series
Topic: AP and GP
Idea tested: Method of Differences (Vn Method)

Same idea in other shifts

Asked 7× in all

5 Apr 2026, Shift 2 · Q5If the sum of the first 10 terms of the series…HardSingle correct
2 Apr 2025, Shift 2 · Q22If the sum of the first 10 terms of the series…HardNumerical value
9 Apr 2024, Shift 1 · Q5If the sum of the series $\frac{1}{1\cdot(1+d)}+\frac{1}{(1+d)(1+2d)}+\ldots+\frac{1}{(1+9d)(1+10d)}$ is equal to $5$ , then $50d$ is equal…MediumSingle correct
6 Apr 2023, Shift 1 · Q8Let $a_1,a_2,a_3,\ldots,a_n$ be $n$ positive consecutive terms of an arithmetic progression. If $d>0$ is its common difference, then…MediumSingle correct
27 Jun 2022, Shift 1 · Q27If the sum of the first ten terms of the series $\frac{1}{5}+\frac{2}{65}+\frac{3}{325}+\frac{4}{1025}+\frac{5}{2501}+\ldots$ is…HardNumerical value
30 Jun 2022, Shift 1 · Q7The value of $1 + \frac{1}{1+2} + \frac{1}{1+2+3} + \ldots + \frac{1}{1+2+3+\ldots+11}$ is equal to :EasySingle correct

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.