The purpose of this exercise is to prove that every Cauchy sequence is a convergent sequence. Let {an} be a Cauchy sequence. (a) Show that {an} is bounded. (b) Show that there is at least one subsequential limit point of {an}. (c) Prove there is no more than one subsequential limit point of {an}. (d) Show that {an} converges
The purpose of this exercise is to prove that every Cauchy sequence is a convergent sequence. Let {an} be a Cauchy sequence. (a) Show that {an} is bounded. (b) Show that there is at least one subsequential limit point of {an}. (c) Prove there is no more than one subsequential limit point of {an}. (d) Show that {an} converges
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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The purpose of this exercise is to prove that every Cauchy sequence is a
convergent sequence. Let {an} be a Cauchy sequence.
(a) Show that {an} is bounded.
(b) Show that there is at least one subsequential limit point of {an}.
(c) Prove there is no more than one subsequential limit point of {an}.
(d) Show that {an} converges
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