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Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
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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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