JEE Main 2021 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 25 July 2021, Shift 1, Maths Q84

Question 84 of 90 in this shift, Maths question 24 of 30, Section B.

If the value of

\left(1+\frac{2}{3}+\frac{6}{3^2}+\frac{10}{3^3}+\ldots\ \text{upto}\ \infty\right)^{\log_{(0.25)}\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\ldots\ \text{upto}\ \infty\right)}

l

, then

l^2

is equal to _________.

Official answer

NTA final key.

Chapter: Sequences and Series
Topic: Arithmetico-Geometric Series
Idea tested: Sum of Infinite AGP

Same idea in other shifts

Asked 5× in all

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27 Jan 2024, Shift 1 · Q24If $8=3+\dfrac{1}{4}(3+p)+\dfrac{1}{4^2}(3+2p)+\dfrac{1}{4^3}(3+3p)+\cdots\cdots\infty$ , then the value of p is ________.MediumNumerical value
29 Jul 2022, Shift 1 · Q24Let $a_1, a_2, a_3, \ldots$ be an A.P. If $\sum_{r=1}^{\infty} \frac{a_r}{2^r} = 4$ , then $4a_2$ is equal to __________.MediumNumerical value
26 Feb 2021, Shift 1 · Q78The sum of the infinite series $1+\frac{2}{3}+\frac{7}{3^2}+\frac{12}{3^3}+\frac{17}{3^4}+\frac{22}{3^5}+\ldots\ldots$ 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.