A sequence of real numbers converges to . Consider the following claims: (I) The sequence converges to . (II) The sequence converges to . Which of the following is correct?
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4 marks, −1MathematicsSequences, series and convergenceSequences and their limitsModerateabout 2 min
DSE 2018 Question 8: Sequences, series and convergence
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A sequence of real numbers (xₙ) converges to x. Consider the following claims: (I) The sequence (xₙ₊₁/xₙ) converges to 1. (II) The sequence (xₙ + xₙ₊₁) converges to 2x. Which of the following is correct? (A) Only statement II is correct (B) Only Statement I is correct (C) None of the statements is correct (D) Both the statements are correct
Also written as: A sequence of real numbers (x_n) converges to x. Consider the following claims: (I) The sequence (x_(n+1)/x_n) converges to 1. (II) The sequence (x_n + x_(n+1)) converges to 2x. Which of the following is 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.
TestStop has 10 past-paper questions on this subtopic.
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Question from the DSE 2018 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.