JEE Main 2023MathematicsSequences and SeriesMediumNumerical

JEE Main 2023 — Sequences and Series Question with Solution

JEE Main 2023 (13 Apr Shift 1)

Question

The sum to 20 terms of the series 2·22-32+2·42-52+2·62-............ is equal to__________.

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Show full solutionCorrect answer: 1310
Correct answer
1310

Step-by-step explanation

Given,

2·22-32+2·42-52+2·62-............20 terms,

=∑r=1102·(2r)2-(2r+1)2

=∑r=1108r2-4r2-4r-1

=∑r=1104r2-4r-1

=4∑r=110r2-4∑r=110r-∑r=1101

=4·10·11·216-410·112-10

=44·35-220-10=1540-230=1310

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About this question

This is a previous-year question from JEE Main 2023, 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.