JEE Main 2022 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 30 June 2022, Shift 1, Maths Q7

Question 7 of 90 in this shift, Maths question 7 of 30, Section A.

The value of

1 + \frac{1}{1+2} + \frac{1}{1+2+3} + \ldots + \frac{1}{1+2+3+\ldots+11}

is equal to :

(1) $\frac{20}{11}$
(2) $\frac{11}{6}$ Official answer
(3) $\frac{241}{132}$
(4) $\frac{21}{11}$

Official answer

Option 2

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
29 Jul 2022, Shift 1 · Q28If…MediumNumerical value
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

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.