(5) 1 کی (a) For all n € N and a + 0, show that (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. Use part (a) to prove that x→x for some x € R. Note: If 0 < b < 1 then b=1 for some a > 1. Then use part (a), since a > 1*0.
(5) 1 کی (a) For all n € N and a + 0, show that (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. Use part (a) to prove that x→x for some x € R. Note: If 0 < b < 1 then b=1 for some a > 1. Then use part (a), since a > 1*0.
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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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
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Use part (a) to prove that Xn x for somex ∈ R. Note: Ifo < b < 1 then b = 12 for some a > 1. Then use
part (a), since a > 1 + 0.
a - 1
1
(a) For alln E Nand a # 0 show that
an
(b) For a sequence (xn) in R, suppose that there exists an be (0, 1 ) such that
[Xn+1 - Xn] ≤ b"
for all nEN.
= 1-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5977e3d6-260f-47f5-8164-3ec7203d88e7%2F909aa236-ef95-4926-b784-82daebac5022%2Fvsh8j346_processed.jpeg&w=3840&q=75)
Transcribed Image Text:J
Use part (a) to prove that Xn x for somex ∈ R. Note: Ifo < b < 1 then b = 12 for some a > 1. Then use
part (a), since a > 1 + 0.
a - 1
1
(a) For alln E Nand a # 0 show that
an
(b) For a sequence (xn) in R, suppose that there exists an be (0, 1 ) such that
[Xn+1 - Xn] ≤ b"
for all nEN.
= 1-
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