Let (an) be an increasing sequence of real numbers. Select all the true statements below. a. If there exists c ER such that an e for all n then (an) is convergent. □b. If an #0 for all n then is decreasing. c. If there exists c ER such that an ≤ c for all n then every subsequence of (a) is convergent.
Let (an) be an increasing sequence of real numbers. Select all the true statements below. a. If there exists c ER such that an e for all n then (an) is convergent. □b. If an #0 for all n then is decreasing. c. If there exists c ER such that an ≤ c for all n then every subsequence of (a) is convergent.
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 73E
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Transcribed Image Text:Let (an) be an increasing sequence of real numbers.
Select all the true statements below.
a.
If there exists c ER such that an c for all n then (an) is convergent.
□ b.
If an #0 for all n then is decreasing.
c.
If there exists c ER such that an ≤ c for all n then every subsequence of (a) is convergent.
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