(b) For a sequence (x) in R, suppose that there exists an b € (0, 1) such that |xn+1-Xn Sb" for all n € N. B Use part (a) to prove that x→x for some x € R. Note: If 0 < b < 1 then b= for some a > 1. Then use part (a), since a > 1 * 0.
(b) For a sequence (x) in R, suppose that there exists an b € (0, 1) such that |xn+1-Xn Sb" for all n € N. B Use part (a) to prove that x→x for some x € R. Note: If 0 < b < 1 then b= for some a > 1. Then use part (a), since a > 1 * 0.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 48E: Let R be the set of all infinite sequences of real numbers, with the operations...
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Please only do this typewritten, so everything is visible. I have a hard time reading handwritten solutions. i hope you understand. thank you. i will upvote
SKIP THIS IF YOU ALREADY DID THIS OR GET DOWNVOTE
Transcribed Image Text:a-1
ANSWER
B ONLY
1
(a) For all n € N and a 0, show that
an
(b) For a sequence (x) in R, suppose that there exists an b € (0, 1) such that
Xn+1-Xn ≤b"
for all n € N.
Use part (a) to prove that x→x for some x € R. Note: If 0 < b < 1 then b = for some a > 1. Then use
part (a), since a > 1 + 0.
= 1-
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