Determine whether the statement is TRUE or FALSE. Justify your answer with a proof or counterexample. If {am} is bounded, then {an} converges. If {an} is monotone, then {an} converges. Every subsequence of a bounded sequence is bounded.

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 71E
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Determine whether the statement is TRUE or FALSE. Justify your answer with a
proof or counterexample.
If {am} is bounded, then {an} converges.
If {an} is monotone, then {an} converges.
Every subsequence of a bounded sequence is bounded.
Transcribed Image Text:Determine whether the statement is TRUE or FALSE. Justify your answer with a proof or counterexample. If {am} is bounded, then {an} converges. If {an} is monotone, then {an} converges. Every subsequence of a bounded sequence is bounded.
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