JEE Main 2023 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 15 April 2023, Shift 1, Maths Q24

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

If the sum of the series

\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{2^2}-\frac{1}{2\cdot3}+\frac{1}{3^2}\right)+\left(\frac{1}{2^3}-\frac{1}{2^2\cdot3}+\frac{1}{2\cdot3^2}-\frac{1}{3^3}\right)+\left(\frac{1}{2^4}-\frac{1}{2^3\cdot3}+\frac{1}{2^2\cdot3^2}-\frac{1}{2\cdot3^3}+\frac{1}{3^4}\right)+\ldots

\frac{\alpha}{\beta}

, where

\alpha

and

\beta

are co-prime, then

\alpha+3\beta

is equal to ______.

Official answer

NTA final key.

Chapter: Sequences and Series
Topic: AP and GP
Idea tested: Infinite GP Sum

Same idea in other shifts

Asked 15× in all

4 Apr 2026, Shift 2 · Q7Let $\alpha=\frac14+\frac18+\frac1{16}+\ldots\infty$ and $\beta=\frac13+\frac19+\frac1{27}+\ldots\infty$ . Then the value of…EasySingle correct
6 Apr 2024, Shift 2 · Q16Let $ABC$ be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle $ABC$ and the…MediumSingle correct
9 Apr 2024, Shift 2 · Q7Let $a, ar, ar^2, \ldots$ be an infinite G.P. If $\sum_{n=0}^{\infty}ar^n=57$ and $\sum_{n=0}^{\infty}a^3r^{3n}=9747$ , then $a+18r$ is…MediumSingle correct
27 Jul 2022, Shift 2 · Q7Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5. Let the sum of its first five terms be…MediumSingle correct
26 Jun 2022, Shift 2 · Q3If $A = \sum_{n=1}^{\infty} \frac{1}{(3 + (-1)^n)^n}$ and $B = \sum_{n=1}^{\infty} \frac{(-1)^n}{(3 + (-1)^n)^n}$ , then $\frac{A}{B}$ is…MediumSingle correct
27 Jun 2022, Shift 1 · Q3If $x=\sum_{n=0}^{\infty} a^n$ , $y=\sum_{n=0}^{\infty} b^n$ , $z=\sum_{n=0}^{\infty} c^n$ , where a, b, c are in A.P. and $|a|<1$ , $|b|<1$ ,…MediumSingle correct
28 Jun 2022, Shift 2 · Q25Let for $n=1, 2, \ldots, 50$ , $S_n$ be the sum of the infinite geometric progression whose first term is $n^2$ and whose common ratio is…HardNumerical value
26 Aug 2021, Shift 1 · Q67If the sum of an infinite GP $a, ar, ar^2, ar^3, \ldots$ is 15 and the sum of the squares of its each term is 150, then the sum of…MediumSingle 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.