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Consider the recursive sequence: 12 απ = 16, an+1 = 12- an-4 (a) Use induction to prove an is bounded below by 8 (b) Use induction to prove an is strictly decreasing. (c) Use the MCT to conclude that an converges. Then finds its limit.

Consider the recursive sequence: 12 απ = 16, an+1 = 12- an-4 (a) Use induction to prove an is bounded below by 8 (b) Use induction to prove an is strictly decreasing. (c) Use the MCT to conclude that an converges. Then finds its limit.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Consider the recursive sequence: 12 απ = 16, an+1 = 12- an-4 (a) Use induction to prove an is bounded below by 8 (b) Use induction to prove an is strictly decreasing. (c) Use the MCT to conclude that an converges. Then finds its limit.
Transcribed Image Text:Consider the recursive sequence: 12 απ = 16, an+1 = 12- an-4 (a) Use induction to prove an is bounded below by 8 (b) Use induction to prove an is strictly decreasing. (c) Use the MCT to conclude that an converges. Then finds its limit.
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