I: | a, - al <ɛ V n z n(ɛ), for any given e > 0. II: | an - aml< e V m, n 2 N, for some NER. III: | a, - aml→ 0 as m, n → o. A. I and II only B. I and III only C. II only D. III only E. None of the above.

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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Which of these statements best describe(s) a, as a Cauchy sequence?
I: | an - al < ɛ V n 2 n(ɛ), for any given ɛ > 0.
II: | an - am|< ɛ vm,n 2 N, for some NER.
III: | a, - aml→ 0 as m,n → o.
A. I and II only
B. I and III only
C. II only
D. II only
E. None of the above.
Transcribed Image Text:Which of these statements best describe(s) a, as a Cauchy sequence? I: | an - al < ɛ V n 2 n(ɛ), for any given ɛ > 0. II: | an - am|< ɛ vm,n 2 N, for some NER. III: | a, - aml→ 0 as m,n → o. A. I and II only B. I and III only C. II only D. II only E. None of the above.
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