i. For a convergent real sequence sn and a real number a, show that if sn ≥ a for all but finitely many values of n, then limn→∞ sn ≥ a.ii. For each value of a ∈ ℝ, give an example of a convergent sequence sn with sn > a for all n, but where limn→∞ sn = a.
i. For a convergent real sequence sn and a real number a, show that if sn ≥ a for all but finitely many values of n, then limn→∞ sn ≥ a.ii. For each value of a ∈ ℝ, give an example of a convergent sequence sn with sn > a for all n, but where limn→∞ sn = a.
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter2: Basic Linear Algebra
Section: Chapter Questions
Problem 15RP
Related questions
Question
i. For a convergent real sequence sn and a real number a, show that if sn ≥ a for all but finitely many values of n, then limn→∞ sn ≥ a.
ii. For each value of a ∈ ℝ, give an example of a convergent sequence sn with sn > a for all n, but where limn→∞ sn = a.
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