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A sequence is a subsequence of if and only if there is an increasingfunction such that

A Transition to Advanced Mathematics | 7th Edition | ISBN: 9780495562023 | Authors: Douglas Smith, Maurice Eggen, Richard St. Andre ISBN: 9780495562023 335

Solution for problem 8 Chapter 4.6

A Transition to Advanced Mathematics | 7th Edition

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A Transition to Advanced Mathematics | 7th Edition | ISBN: 9780495562023 | Authors: Douglas Smith, Maurice Eggen, Richard St. Andre

A Transition to Advanced Mathematics | 7th Edition

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Problem 8

A sequence is a subsequence of if and only if there is an increasingfunction such that For example, is thesequence whose terms are just the even-numbered term of the sequence(a) Let Describe the subsequences and(b) Prove that if a sequence x converges to L then for every real thereexists a subsequence y of x such that for all(c) Prove that if converges to L and is a subsequence of x, then y convergesto L.(d) Prove that if x contains two convergent subsequences y and z,and and then x diverges.

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Chapter 4.6, Problem 8 is Solved
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Textbook: A Transition to Advanced Mathematics
Edition: 7
Author: Douglas Smith, Maurice Eggen, Richard St. Andre
ISBN: 9780495562023

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A sequence is a subsequence of if and only if there is an increasingfunction such that