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
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 55E
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a0802a2-9dd1-43c0-9b3f-3c3accbadbd6%2Feded4f3e-13e2-47ed-aa13-d432a2ce9e14%2Folc1iqi_processed.jpeg&w=3840&q=75)
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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