2. SUBSEQUENCES (a) Let (r) be a sequence and let (n) be a subsequence. Show that if (n) is monotone increasing, then (n) is monotone increasing. -1 (b) Let (n) be a sequence. Assume that (n) has two subsequences that converge to different real numbers. Show that (n) does not converge.
2. SUBSEQUENCES (a) Let (r) be a sequence and let (n) be a subsequence. Show that if (n) is monotone increasing, then (n) is monotone increasing. -1 (b) Let (n) be a sequence. Assume that (n) has two subsequences that converge to different real numbers. Show that (n) does not converge.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 5RE
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Transcribed Image Text:2. SUBSEQUENCES
(a) Let (₂) be a sequence and let (n) be a subsequence. Show that if (n) is
=1
k=1
increasing, then (n) is monotone increasing.
be a sequence. Assume that (n) has two subsequences that converge to
different real numbers. Show that (n) does not converge.
monotone
(b) Let (n)
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