Unformatted text preview: 2. Give an example of each of the following, or argue that such a request is impossible. a. A Cauchy sequence that is not monotone b. A monotone sequence that is not Cauchy c. A Cauchy sequence with a divergent subsequence d. An unbounded sequence containing a subsequence that is Cauchy 3. Give an proof to verify that 4. Does the sequence defined by converge (to a finite number)? Either find its limit and verify it, or prove that the limit does not exist. 5. Let and let for all positive integers n . Prove converges. 6. Prove that every bounded sequence has a convergent subsequence. \...
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- Spring '08
- Math, Mathematical analysis, Cauchy sequence, Cauchy