(a) For all ne N and a # 0, show that (b) For a sequence (xn) in R, 1 an k=1 suppose that there exists an b € (0, 1) such that |xn+1-Xn ≤ b for all n € N. Use part (a) to prove that xnx for some x € R. Note: If 0 < b < 1 then b = for some a > 1. Then use part (a), since a > 1 + 0. a-1 ak MOTO = 1
(a) For all ne N and a # 0, show that (b) For a sequence (xn) in R, 1 an k=1 suppose that there exists an b € (0, 1) such that |xn+1-Xn ≤ b for all n € N. Use part (a) to prove that xnx for some x € R. Note: If 0 < b < 1 then b = for some a > 1. Then use part (a), since a > 1 + 0. a-1 ak MOTO = 1
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 23E
Related questions
Question
![a-1
ak
1
an
= 1
(a) For all ne N and a # 0, show that
k=1
(b) For a sequence (xn) 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 xnx for some x € R. Note: If 0 < b < 1 then b = for some a > 1. Then use
part (a), since a > 1 + 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F345814fa-de43-4c36-b40c-28f9a134eaa3%2Fb9cd284d-6856-4b2a-bfff-6acc6dd09229%2Fhywi8ad_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a-1
ak
1
an
= 1
(a) For all ne N and a # 0, show that
k=1
(b) For a sequence (xn) 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 xnx for some x € R. Note: If 0 < b < 1 then b = for some a > 1. Then use
part (a), since a > 1 + 0.
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