JEE Main 2021MathematicsSequences and SeriesMediumNumerical

JEE Main 2021 — Sequences and Series Question with Solution

JEE Main 2021 (25 Jul Shift 1)

Question

If the value of 1+23+632+1033+….. upto ∞log0.2513+132+133+…. upto ∞ is l, then l2 is equal to             .

Enter your answer

Show full solutionCorrect answer: 3
Correct answer
3

Step-by-step explanation

l=1+23+632+1033+….. upto ∞log0.2513+132+133+…. upto ∞

Assume, S=1+23+632+1033+….. upto ∞

S=1+23+632+1033+…-S3=13+232+633+…2S3=1+13+432+433+…

2S3=43+432+433+….

S=32431-13=3

Now l=3log0.25131-13

l=3log1412=312=3

⇒l2=3

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Sequences and Series chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2021, covering the Sequences and Series chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.