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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 30E
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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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