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.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
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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.
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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