(1) Let (an) be the sequence given by an = (a) Show that for all ɛ > 0 there is N E N where = √n. an+1 an < & for all n > N. (b) Show that (an) is not Cauchy (Hint: there is a short way and a long way to do this. You are allowed to refer to results from the lectures)

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.1: Sequences And Their Notations
Problem 69SE: Find a recursive formula for the sequence 1,0,1,1,0,1,1,0,1,1,0,1,1,... (Hint: find a pattern for an...
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(1) Let (an) be the sequence given by an
√n.
(a) Show that for all ɛ > 0 there is N E N where
=
an+1 an < & for all n > N.
(b) Show that (an) is not Cauchy (Hint: there is a short way and a long way to
do this. You are allowed to refer to results from the lectures)
Transcribed Image Text:(1) Let (an) be the sequence given by an √n. (a) Show that for all ɛ > 0 there is N E N where = an+1 an < & for all n > N. (b) Show that (an) is not Cauchy (Hint: there is a short way and a long way to do this. You are allowed to refer to results from the lectures)
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