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Questions › DSE › DSE 2007 › Q43
2 marksMathematics › Sequences, series and convergence › Sequences and their limitsModerateabout 2 min

DSE 2007 Question 43: Sequences, series and convergence

The sequence (xn)(x_{n})(xn​), where xn=(−1)n(1+n−1)x_{n}=(-1)^{n}(1+n^{-1})xn​=(−1)n(1+n−1) and n=1,2,…n=1,2,\ldotsn=1,2,…

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Plain-text version

The sequence (xₙ), where xₙ=(-1)ⁿ(1+n⁻¹) and n=1,2,… (A) converges to 1 (B) converges to -1 (C) converges to 1 and -1 (D) converges to neither 1 nor -1

Also written as: The sequence (x_n), where x_n=(-1)^n(1+n^(-1)) and n=1,2,...

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.

TestStop has 10 past-paper questions on this subtopic.

Practise Sequences, series and convergenceMore on Sequences and their limits

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Question from the DSE 2007 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.