Learn

Friday, 9 October

JEE Main Maths · Sequences and Series

Infinite GP Sum

Infinite GP Sum (Sequences and Series) was asked 5 times in 5 JEE Main shifts, 2020–2026, out of the 42 shifts Lumi analysed.

Times asked
5
in 5 shifts
Years
2020–2026
Usual format
Single correct
Multi-step
Pattern
Frequent
repeats across shifts

How it is asked

  • Value from infinite gp sums and logs
  • Unknown terms from infinite gp sums

Difficulty

Easy 2Medium 3Hard 0

Where it sits

Chapter: Sequences and Series. Topic: AP and GP, 59 questions over 17 ideas.

Other repeat ideas in this topic

Every time it came

All 5 questions

Newest first, each with its options and official answer.

  1. 4 Apr 2026, Shift 2 · Q7Let α=14+18+116+…∞\alpha=\frac14+\frac18+\frac1{16}+\ldots\infty and β=13+19+127+…∞\beta=\frac13+\frac19+\frac1{27}+\ldots\infty. Then the value of…EasySingle correct
  2. 6 Apr 2024, Shift 2 · Q16Let ABCABC be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle ABCABC and the…MediumSingle correct
  3. 9 Apr 2024, Shift 2 · Q7Let a,ar,ar2,…a, ar, ar^2, \ldots be an infinite G.P. If ∑n=0∞arn=57\sum_{n=0}^{\infty}ar^n=57 and ∑n=0∞a3r3n=9747\sum_{n=0}^{\infty}a^3r^{3n}=9747, then a+18ra+18r is…MediumSingle correct
  4. 9 Jan 2020, Shift 2 · Q69If x=∑n=0∞(−1)ntan⁡2nθx=\sum_{n=0}^{\infty}(-1)^n\tan^{2n}\theta and y=∑n=0∞cos⁡2nθy=\sum_{n=0}^{\infty}\cos^{2n}\theta, for 0<θ<π40<\theta<\frac{\pi}{4}, then :EasySingle correct
  5. 2 Sep 2020, Shift 1 · Q58If ∣x∣<1|x|<1, ∣y∣<1|y|<1 and x≠yx\neq y, then the sum to infinity of the following series…MediumSingle correct