*? Let (sn) be a sequence that converges. (a) Show that if sn > a for all but finitely many n, then lim sn > a. (b) Show that if sn
*? Let (sn) be a sequence that converges. (a) Show that if sn > a for all but finitely many n, then lim sn > a. (b) Show that if sn
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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![8.9 *? Let (sn) be a sequence that converges.
(a) Show that if sn > a for all but finitely many n, then lim s,n 2 a.
(b) Show that if sn <b for all but finitely many n, then lim s, < b.
(c) Conclude that if all but finitely many sn belong to [a, b], then
lim s, belongs to [a, b].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c99a240-9de7-4947-9b54-53ff2cf6c85e%2F25563bcf-b3e0-46f7-a47e-0fb410b41fe0%2Fuma0nik_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8.9 *? Let (sn) be a sequence that converges.
(a) Show that if sn > a for all but finitely many n, then lim s,n 2 a.
(b) Show that if sn <b for all but finitely many n, then lim s, < b.
(c) Conclude that if all but finitely many sn belong to [a, b], then
lim s, belongs to [a, b].
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