A) If (xn) is a decreasing and bounded sequence. Prove that (x,n) is convergent with lim xn inf {xn :n E N} %3D 1 B) By using (A), Find lim 72 8 yn C) Prove that a Cauchy sequence of real numbers is bounded.
A) If (xn) is a decreasing and bounded sequence. Prove that (x,n) is convergent with lim xn inf {xn :n E N} %3D 1 B) By using (A), Find lim 72 8 yn C) Prove that a Cauchy sequence of real numbers is bounded.
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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Transcribed Image Text:A) If (xn) is a decreasing and bounded sequence. Prove that (x,n) is convergent with
lim xn =
inf (xn n E N}
B) By using (A), Find lim
no yn
C) Prove that a Cauchy sequence of real numbers is bounded.
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