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(b) Let (an) be a Cauchy sequence such that a, 0 for every n. Is it always true that is also Cauchy sequence? Justify your answer. (Prove if true, give a counterexample if not.)

(b) Let (an) be a Cauchy sequence such that a, 0 for every n. Is it always true that is also Cauchy sequence? Justify your answer. (Prove if true, give a counterexample if not.)

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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5. (a) Give a definition of a Cauchy sequence. (b) Let (an) be a Cauchy sequence such that a, #0 for every n. Is it always true that is also Cauchy sequence? Justify your answer. an (Prove if true, give a counterexample if not.) (c) Suppose that for each n e N, 1. Int1 Inl S 2n Prove that (z,) is Cauchy and deduce that (z) converges.
Transcribed Image Text:5. (a) Give a definition of a Cauchy sequence. (b) Let (an) be a Cauchy sequence such that a, #0 for every n. Is it always true that is also Cauchy sequence? Justify your answer. an (Prove if true, give a counterexample if not.) (c) Suppose that for each n e N, 1. Int1 Inl S 2n Prove that (z,) is Cauchy and deduce that (z) converges.
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