Let sn be a bounded sequence, and let tn converge to L. i. Show that if L = 0, then the product sn ⋅ tn also converges to 0. ii. Give an example where sn is bounded and tn converges, but where the product does not converge.
Let sn be a bounded sequence, and let tn converge to L. i. Show that if L = 0, then the product sn ⋅ tn also converges to 0. ii. Give an example where sn is bounded and tn converges, but where the product does not converge.
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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Question
Let sn be a bounded sequence, and let tn converge to L.
i. Show that if L = 0, then the product sn ⋅ tn also converges to 0.
ii. Give an example where sn is bounded and tn converges, but where the product does not converge.
Hint: One approach to (i) uses the Sandwich Theorem.
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