15 Let (a,) be a sequence of real numbers. Which of the following statements about (a,) is true? O a. if (a,) has a convergent subsequence, then (a,) is Cauchy. O b. if (a,) is Cauchy then the sequence 1 is convergent a,-1 in O c. if la, <2 for all n 2 13 then (a,) has a Cauchy subsequence. d. none of the listed statements is true

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 25E
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15
Let (a,) be a sequence of real numbers. Which of the following statements about (a,) is true?
O a. if (a,) has a convergent subsequence, then (a,) is Cauchy.
O b.
if (a,) is Cauchy then the sequence
1
is convergent
a,-1
in
O c. if la, <2 for all n 2 13 then (a,) has a Cauchy subsequence.
O d.
none of the listed statements is true
Transcribed Image Text:15 Let (a,) be a sequence of real numbers. Which of the following statements about (a,) is true? O a. if (a,) has a convergent subsequence, then (a,) is Cauchy. O b. if (a,) is Cauchy then the sequence 1 is convergent a,-1 in O c. if la, <2 for all n 2 13 then (a,) has a Cauchy subsequence. O d. none of the listed statements is true
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