Let (an), (bn) and (cn) be three bounded sequences with an ≤ bn ≤ Cn for each n. Prove that if lim sup en ≤ lim infan, then all three sequences converge and lim anlim bn n→∞0 n+→∞0 = lim Cn. n→∞0
Let (an), (bn) and (cn) be three bounded sequences with an ≤ bn ≤ Cn for each n. Prove that if lim sup en ≤ lim infan, then all three sequences converge and lim anlim bn n→∞0 n+→∞0 = lim Cn. n→∞0
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 34E
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