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Questions › IIT JAM › IIT JAM 2023 › Q18
2 marks, −0.667Mathematics › Sequences, series and convergence › Sequences and their limitsHardabout 3 min

IIT JAM 2023 Question 18: Sequences, series and convergence

Let an=(1+1n)n/2a_n=\left(1+\tfrac1n\right)^{n/2}an​=(1+n1​)n/2 be the nnnth term of ⟨an⟩\langle a_n\rangle⟨an​⟩. Which one is NOT CORRECT?

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Let aₙ=(1+1/n)^(n/2) be the n th term of ⟨ aₙ⟩. Which one is NOT CORRECT? (A) ⟨ aₙ⟩ is bounded (B) ⟨ aₙ⟩ is increasing (C) Σₙ₌₁^∞ln (aₙ) is a convergent series (D) lim_(n→∞)(1/nΣₖ₌₁ⁿaₖ)=√e

Also written as: Let a_n=(1+1/n)^(n/2) be the n th term of < a_n>. Which one is NOT CORRECT?

Sequences, series and convergence has come up 33 times in 5 exams since 2006.

What this question tests

This question is on Sequences and their limits, part of Sequences, series and convergence in Mathematics.

Whether a sequence settles down and what it settles to.

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Question from the IIT JAM 2023 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.