4. Let a < b. Let x¡ = a, x2 = b, and Xn+1+Xn Xn+2 = for n > 1. 2 Follow these steps to show that (x„)n€N is Cauchy. (a) Draw a picture and let L = b – a. (b) Use induction to show that xn+1 – Xn] = L/2"-1 for each n. %3D
4. Let a < b. Let x¡ = a, x2 = b, and Xn+1+Xn Xn+2 = for n > 1. 2 Follow these steps to show that (x„)n€N is Cauchy. (a) Draw a picture and let L = b – a. (b) Use induction to show that xn+1 – Xn] = L/2"-1 for each n. %3D
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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QUESTION 4B PLEASE
(4A HAS BEEN SOLVED ALREADY)
![4. Let a < b. Let x = a, x2 = b, and
Xn+1 +Xn
Xn+2 =
for n 2 1.
2
Follow these steps to show that (x,)neN is Cauchy.
(a) Draw a picture and let L = b- a.
(b) Use induction to show that xn+1 – Xn] = L/2"- for each n.
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd95b1c5e-3673-40a0-a87b-179a3e73672c%2F51b9f53c-e629-4040-9d15-5bc1bf3b78a1%2Ff4lhxuf_processed.png&w=3840&q=75)
Transcribed Image Text:4. Let a < b. Let x = a, x2 = b, and
Xn+1 +Xn
Xn+2 =
for n 2 1.
2
Follow these steps to show that (x,)neN is Cauchy.
(a) Draw a picture and let L = b- a.
(b) Use induction to show that xn+1 – Xn] = L/2"- for each n.
%3D
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