JEE Main 2017MathematicsSequences and SeriesHardMCQ

JEE Main 2017 — Sequences and Series Question with Solution

JEE Main 2017 (09 Apr Online)

Question

Let Sn=113+1+213+23+1+2+313+23+33+…+1+2+…,+n13+23+…n3 . If 100 Sn=n, then n is equal to:

Choose an option

Show full solutionCorrect option: B
Correct answer
B199

Step-by-step explanation

Given, Sn=113+1+213+23+1+2+313+23+33+…+1+2+…+n13+23+…+n3

Tn=nn+12nn+122

Tn=2nn+1=21n-1n+1

Sn=2∑n=1n1n-1n+1

Sn=21-1n+1=2nn+1

Given, 100Sn=n⇒100×2nn+1=n

n+1=200

n=199

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About this question

This is a previous-year question from JEE Main 2017, 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.