Suppose (an ) is Cauchy and that for all m, k ≥ 100, |am − ak | < 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 − ak | < 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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Topic Video
Question
Suppose (an ) is Cauchy and that for all m, k ≥ 100, |am − ak | < 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
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images