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The set from problem 1 is a_(n+1)=sqrt(3+2*a_n), where a_1=1 For problem 2, it shows that A is not bounded above when a>1, where A= {a^n | n € N} ={a, a^2, a^3, ...} 3. Let A be the set of all the real numbers a, from problem 1. Prove that sup(A) = 3. [Hint: Define an 3-an, and use the result from problem 2 to show that for every c> 0, there is a positive integer n such that an < c.] H

The set from problem 1 is a_(n+1)=sqrt(3+2*a_n), where a_1=1 For problem 2, it shows that A is not bounded above when a>1, where A= {a^n | n € N} ={a, a^2, a^3, ...} 3. Let A be the set of all the real numbers a, from problem 1. Prove that sup(A) = 3. [Hint: Define an 3-an, and use the result from problem 2 to show that for every c> 0, there is a positive integer n such that an < c.] H

Advanced Engineering Mathematics
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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The set from problem 1 is a_(n+1)=sqrt(3+2*a_n), where a_1=1 - For problem 2, it shows that A is not bounded above when a>1, where A= {a^n | n € N} ={a, a^2, a^3, ...} 3. Let A be the set of all the real numbers a, from problem 1. Prove that sup(A) = 3. [Hint: Define c = 3 ans and use the result from problem 2 to show that for every c> 0, there is a positive integer n such that an < c.]
Transcribed Image Text:The set from problem 1 is a_(n+1)=sqrt(3+2*a_n), where a_1=1 - For problem 2, it shows that A is not bounded above when a>1, where A= {a^n | n € N} ={a, a^2, a^3, ...} 3. Let A be the set of all the real numbers a, from problem 1. Prove that sup(A) = 3. [Hint: Define c = 3 ans and use the result from problem 2 to show that for every c> 0, there is a positive integer n such that an < c.]
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