JEE Main 2021MathematicsSequences and SeriesEasyMCQ

JEE Main 2021 — Sequences and Series Question with Solution

JEE Main 2021 (26 Feb Shift 2)

Question

If 0<a,b<1, and tan-1a+tan-1b=π4, then the value of a+b-a2+b22+a3+b33-a4+b44+… is :

Choose an option

Show full solutionCorrect option: D
Correct answer
Dloge2

Step-by-step explanation

tan-1a+tan-1 b=π4 0<a,b<1

⇒a+b1-ab=1

a+b=1-ab

a+1b+1=2

Now a-a22+a33+…+b-b22+b33+…

=loge1+a+loge1+b

(∵ expansion of loge1+x)

=loge1+a1+b

=loge2

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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.