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1 an + Show that the sequence {an} is convergent - Let aj > 0 and an+1 = An Hint: Use the item 1 of Homework 1 to show that an> V4, Vn E N. Then use induction to show that an > 0, Vn e N. To show that the sequence is monotonic, investigate an+1 - an.

1 an + Show that the sequence {an} is convergent - Let aj > 0 and an+1 = An Hint: Use the item 1 of Homework 1 to show that an> V4, Vn E N. Then use induction to show that an > 0, Vn e N. To show that the sequence is monotonic, investigate an+1 - an.

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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1 1. Let a1 > 0 and an+1 4 An + An Show that the sequence {an} is convergent Hint: Use the item 1 of Homework 1 to show that an > V4, Vn E N. Then use induction to show that an > 0, Vn E N. To show that the sequence is monotonic, investigate an+1 - an.
Transcribed Image Text:1 1. Let a1 > 0 and an+1 4 An + An Show that the sequence {an} is convergent Hint: Use the item 1 of Homework 1 to show that an > V4, Vn E N. Then use induction to show that an > 0, Vn E N. To show that the sequence is monotonic, investigate an+1 - an.
ITEM 1 of HOMEWORK 1 1. Using the axioms and theorems discussed in Lecture Notes Section 1.1, show that Vab s2 a +b for any a, b eR with a > 0 and b> 0.
Transcribed Image Text:ITEM 1 of HOMEWORK 1 1. Using the axioms and theorems discussed in Lecture Notes Section 1.1, show that Vab s2 a +b for any a, b eR with a > 0 and b> 0.
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