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Unformatted text preview: { a n } is an unbounded sequence of positive numbers, then { a n } has a subsequence that diverges to inﬁnity. 9.4: Consider the sequence deﬁned by setting a = 2 and a n +1 = a na 2 n2 2 a n . What is lim n →∞ a n ? 9.5: Using only the deﬁnition, prove that the sequence a n = 1 n is a Cauchy sequence. 9.6: Problem 2.13.2 (a,b,c,e) 9.7: Problem 2.13.9 9.8: Prove that lim sup n →∞ a n = ∞ if and only if { a n } has no upper bound. 1...
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This note was uploaded on 03/18/2012 for the course MAT MAT 25 taught by Professor Stevenklee during the Fall '10 term at UC Davis.
 Fall '10
 StevenKlee
 Calculus

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