Let (xn) be bounded, and lim (xn – xn+1) = 0. Let L = lim inf rn and H = lim sup xn. Show that every n00 n00 n00 number in the interval [L, H] is a limit point for (xn).
Let (xn) be bounded, and lim (xn – xn+1) = 0. Let L = lim inf rn and H = lim sup xn. Show that every n00 n00 n00 number in the interval [L, H] is a limit point for (xn).
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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![Let (xn) be bounded, and lim (xn – xn+1) = 0. Let L = lim inf rn and H = lim sup xn. Show that every
n00
n 00
n00
number in the interval [L, H] is a limit point for (xn).
Hint: prove by contradiction.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdd169baa-5775-4013-8da2-28371ec288c4%2F33d5300e-9fb2-461a-b2c2-522e06ccf378%2F6odojt5_processed.png&w=3840&q=75)
Transcribed Image Text:Let (xn) be bounded, and lim (xn – xn+1) = 0. Let L = lim inf rn and H = lim sup xn. Show that every
n00
n 00
n00
number in the interval [L, H] is a limit point for (xn).
Hint: prove by contradiction.
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