JEE Main 2022MathematicsSequences and SeriesHardNumerical

JEE Main 2022 — Sequences and Series Question with Solution

JEE Main 2022 (27 Jul Shift 2)

Question

23-131×7+43-33+23-132×11+63-53+43-33+23-133×15+…..+303-293+283-273+…+23-1315×63 is equal to ______.

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Show full solutionCorrect answer: 120
Correct answer
120

Step-by-step explanation

Given series, 23-131×7+43-33+23-132×11+63-53+43-33+23-133×15+…..+303-293+283-273+…+23-1315×63 

Now finding Tn=∑k=1n2k3-2k-13n4n+3

=∑k=1n4k2+2k-12+2k2k-1n4n+3

=∑k=1n12k2-6k+1n4n+3

=2n2n2+3n+1-3n2-3n+nn4n+3

=n24n+3n4n+3=n

So,Tn=n

Now finding Sn=∑n=115Tn=15×162=120

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About this question

This is a previous-year question from JEE Main 2022, 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.