JEE Main 2020MathematicsLimitsMediumNumerical

JEE Main 2020 — Limits Question with Solution

JEE Main 2020 (02 Sep Shift 1)

Question

If limx→1x+x2+x3+...+xn-nx-1=820, n∈N then the value of n is equal to....

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Show full solutionCorrect answer: 40
Correct answer
40

Step-by-step explanation

 limx→1x+x2+x3+….+xn-nx-1=820         00form

Applying L'Hospital rule

limx→11+2x+3x2+…..+nxn-11=820

⇒1+2+3+……+n=820

⇒n(n+1)2=820

⇒n2+n=1640

⇒n2+n-1640=0

⇒n=40, -41

Since n is natural number ⇒n=40.

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About this question

This is a previous-year question from JEE Main 2020, covering the Limits 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.