1. Every convergent sequence is bounded. 2. If (s) is a convergent sequence with lims, = s and (t) is a subsequence of (s), then (t) is convergent and lim = C
1. Every convergent sequence is bounded. 2. If (s) is a convergent sequence with lims, = s and (t) is a subsequence of (s), then (t) is convergent and lim = C
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Prove or disprove:
Transcribed Image Text:1. Every convergent sequence is bounded.
2. If \((s_n)\) is a convergent sequence with \(\lim s_n = s\) and \((t_n)\) is a subsequence of \((s_n)\), then \((t_n)\) is convergent and \(\lim t_n = s\).
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