JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 2 September 2020, Shift 1, Maths Q58

Question 58 of 75 in this shift, Maths question 8 of 25.

|x|<1

|y|<1

and

x\neq y

, then the sum to infinity of the following series

(x+y)+(x^{2}+xy+y^{2})+(x^{3}+x^{2}y+xy^{2}+y^{3})+\ldots

is :

(1) $\frac{x+y+xy}{(1+x)(1+y)}$
(2) $\frac{x+y+xy}{(1-x)(1-y)}$
(3) $\frac{x+y-xy}{(1-x)(1-y)}$ Official answer
(4) $\frac{x+y-xy}{(1+x)(1+y)}$

Official answer

Option 3

NTA final key (Sep 2020).

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

Same idea in other shifts

Asked 5× in all

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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 42 of the 174 JEE Main shifts held from 2017 to 2026.