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Which of the following sequences is both non-convergent and contains a Cauchy subsequence? a. (0, -2, 1, 4, 2, −6, 3, -8, 4, ...). b. (1, 2, 3, 4, 5, ...). c. None of them, as a Cauchy sequence must converge. d. (0, 1, 0, 2, 0, 3, . . .).

Which of the following sequences is both non-convergent and contains a Cauchy subsequence? a. (0, -2, 1, 4, 2, −6, 3, -8, 4, ...). b. (1, 2, 3, 4, 5, ...). c. None of them, as a Cauchy sequence must converge. d. (0, 1, 0, 2, 0, 3, . . .).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Which of the following sequences is both non-convergent and contains a Cauchy subsequence? a. (0, -2, 1,-4, 2, -6, 3, -8, 4, ...). b. (1, 2, 3, 4, 5, ...). c. None of them, as a Cauchy sequence must converge. d. (0, 1, 0, 2, 0, 3, . . .).
Transcribed Image Text:Which of the following sequences is both non-convergent and contains a Cauchy subsequence? a. (0, -2, 1,-4, 2, -6, 3, -8, 4, ...). b. (1, 2, 3, 4, 5, ...). c. None of them, as a Cauchy sequence must converge. d. (0, 1, 0, 2, 0, 3, . . .).
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