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Given a positive sequence {a,}n>o satisfying Vai > yao + 1 ana a < 1 An+1 an-1 for any positive integer n, show that An+1 an converges as n → 0. Show moreover that a,0¬" converges as n → 00, where O is the limit of the sequence an+1/an-

Given a positive sequence {a,}n>o satisfying Vai > yao + 1 ana a < 1 An+1 an-1 for any positive integer n, show that An+1 an converges as n → 0. Show moreover that a,0¬" converges as n → 00, where O is the limit of the sequence an+1/an-

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 72E
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Given a positive sequence {an},>0 satisfying Vaị > vao + 1 ana a < 1 аn-1 An+1 for any positive integer n, show that an+1 An converges as n → 0. Show moreover that a„0¬" converges as n → ∞, O is the limit of the sequence an+1/an. where
Transcribed Image Text:Given a positive sequence {an},>0 satisfying Vaị > vao + 1 ana a < 1 аn-1 An+1 for any positive integer n, show that an+1 An converges as n → 0. Show moreover that a„0¬" converges as n → ∞, O is the limit of the sequence an+1/an. where
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