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Questions › DSE › DSE 2014 › Q1
1 mark, −0.333333333333333Mathematics › Sequences, series and convergence › Sequences and their limitsModerateabout 2 min

DSE 2014 Question 1: Sequences, series and convergence

Let an=(1+1n)n+1a_n=\left(1+\tfrac{1}{n}\right)^{n+1}an​=(1+n1​)n+1, n=1,2,…n=1,2,\dotsn=1,2,…. Then the sequence (an)n=1∞(a_n)_{n=1}^\infty(an​)n=1∞​

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Let aₙ=(1+1/n)ⁿ⁺¹, n=1,2,…. Then the sequence (aₙ)ₙ₌₁^∞ (A) is an increasing sequence (B) first increases, then decreases (C) is a decreasing sequence (D) first decreases, then increases

Also written as: Let a_n=(1+1/n)^(n+1), n=1,2,.... Then the sequence (a_n)_(n=1)^(inf)

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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Practise Sequences, series and convergenceMore on Sequences and their limits

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Question from the DSE 2014 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.