JEE Main 2022 · MathsNumerical answerNumerical valueHardCalculation

JEE Main 28 June 2022, Shift 2, Maths Q25

Question 25 of 90 in this shift, Maths question 25 of 30, Section B.

Let 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

\frac{1}{(n+1)^2}

. Then the value of

\frac{1}{26}+\sum_{n=1}^{50}\left(S_n+\frac{2}{n+1}-n-1\right)

is equal to __________.

Official answer

41651

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
15 Apr 2023, Shift 1 · Q24If the sum of the series…HardNumerical value
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
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.