a (a) For all ne N and a # 0, show that an k=1 (b) For a sequence (xn) in R, suppose that there exists an b € (0, 1) such that Xn+1-Xn ≤b" for all n € N. Use part (a) to prove that xnx for some x € R. Note: If 0 < b < 1 then b = for some a > 1. Then use part (a), since a > 10. 1-
a (a) For all ne N and a # 0, show that an k=1 (b) For a sequence (xn) in R, suppose that there exists an b € (0, 1) such that Xn+1-Xn ≤b" for all n € N. Use part (a) to prove that xnx for some x € R. Note: If 0 < b < 1 then b = for some a > 1. Then use part (a), since a > 10. 1-
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 55E: The Fibonacci sequence fn=1,1,2,3,5,8,13,21,... is defined recursively by f1=1,f2=1,fn+2=fn+1+fn for...
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