JEE Main 2023 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 11 April 2023, Shift 2, Maths Q23

Question 23 of 90 in this shift, Maths question 23 of 30, Section B.

For

k \in \mathbb{N}

, if the sum of the series

1 + \frac{4}{k} + \frac{8}{k^2} + \frac{13}{k^3} + \frac{19}{k^4} + \ldots

10

, then the value of

k

is ________

Official answer

NTA final key.

Chapter: Sequences and Series
Topic: Arithmetico-Geometric Series
Idea tested: Second-Order AGP Summation

Same idea in other shifts

Asked 4× in all

27 Jun 2022, Shift 2 · Q5Let $S=2+\frac{6}{7}+\frac{12}{7^2}+\frac{20}{7^3}+\frac{30}{7^4}+\dots..$ Then $4S$ is equal toMediumSingle correct
29 Jun 2022, Shift 2 · Q4The sum of the infinite series…MediumSingle correct
31 Aug 2021, Shift 2 · Q84If $\mathrm{S} = \frac{7}{5}+\frac{9}{5^2}+\frac{13}{5^3}+\frac{19}{5^4}+...$ , then $160\,\mathrm{S}$ is equal to ______________.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.