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(b) Let (an) be a sequence such that a₁ = 2 and an+1 =√√an for all nЄN. Show that: (i) 1 < an ≤2 for all nЄ N, (ii) the sequence (an) is decreasing, (iii) the sequence (an) has a limit. Hence or otherwise, find lim an 170

(b) Let (an) be a sequence such that a₁ = 2 and an+1 =√√an for all nЄN. Show that: (i) 1 < an ≤2 for all nЄ N, (ii) the sequence (an) is decreasing, (iii) the sequence (an) has a limit. Hence or otherwise, find lim an 170

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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(b) Let (an) be a sequence such that a₁ = 2 and an+1 =√√an for all nЄN. Show that: (i) 1 < an ≤2 for all nЄ N, (ii) the sequence (an) is decreasing, (iii) the sequence (an) has a limit. Hence or otherwise, find lim an 170
Transcribed Image Text:(b) Let (an) be a sequence such that a₁ = 2 and an+1 =√√an for all nЄN. Show that: (i) 1 < an ≤2 for all nЄ N, (ii) the sequence (an) is decreasing, (iii) the sequence (an) has a limit. Hence or otherwise, find lim an 170
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