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(d) A Cauchy sequence with an unbounded subsequence. (e) An unbounded seuqence with a Cauchy subsequence.

(d) A Cauchy sequence with an unbounded subsequence. (e) An unbounded seuqence with a Cauchy subsequence.

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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please just answer part d & e

For each of the following, give an example of a sequence with that property and justify why it does so, or else prove that no such sequence exists: (a) A sequence that has a subsequence converging to 7, a subsequence converging to 17, and a subsequence converging to T. (b) A convergent sequence with an increasing subsequence and a decreasing subsequence. (c) A sequence with no convergent subsequences. (d) A Cauchy sequence with an unbounded subsequence. (e) An unbounded seuqence with a Cauchy subsequence.
Transcribed Image Text:For each of the following, give an example of a sequence with that property and justify why it does so, or else prove that no such sequence exists: (a) A sequence that has a subsequence converging to 7, a subsequence converging to 17, and a subsequence converging to T. (b) A convergent sequence with an increasing subsequence and a decreasing subsequence. (c) A sequence with no convergent subsequences. (d) A Cauchy sequence with an unbounded subsequence. (e) An unbounded seuqence with a Cauchy subsequence.
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