Suppose (an ) is Cauchy and that for all m, k ≥ 100, |am − a k | < 1/4. Let ε > 0. Does it follow that the interval (a100 − ε, a100 + ε) contains infinitely many terms of (an )? Either show that it does or give a counter-example

Suppose (an ) is Cauchy and that for all m, k ≥ 100, |am − a k | < 1/4. Let ε > 0. Does it follow that the interval (a100 − ε, a100 + ε) contains infinitely many terms of (an )? Either show that it does or give a counter-example

Name: Suppose (an ) is Cauchy and that for all m, k ≥ 100, |am − a k | < 1/4
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Description: Suppose (an ) is Cauchy and that for all m, k ≥ 100, |am − a k | 0. Does it follow thatthe interval (a100 − ε, a100 + ε) contains infinitely many terms of (an )?Either show that it does or give a counter-example

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.5: Graphs Of Functions

Problem 56E

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