Suppose a Cauchy sequence {xn} is such that for every M ∈ N, there exists a k ≥ M and an n ≥ M such that xk < 0 and xn > 0. Using simply the definition of a Cauchy sequence and of a convergent sequence, show that the sequence converges to 0.
Suppose a Cauchy sequence {xn} is such that for every M ∈ N, there exists a k ≥ M and an n ≥ M such that xk < 0 and xn > 0. Using simply the definition of a Cauchy sequence and of a convergent sequence, show that the sequence converges to 0.
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 25E
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Suppose a Cauchy sequence {xn} is such that for every M ∈ N, there exists a k ≥ M and an n ≥ M such that xk < 0 and xn > 0. Using simply the definition of a Cauchy sequence and of a convergent sequence, show that the sequence converges to 0.
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