Given a sequence x₁, x2,... of real numbers, show that cos(x₁) + + cos(xn) exists if and only if exists. lim 81x lim n→∞ n cos(x₁) + cos(x4) + ... + cos(x²) n²

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.4: Fractional Expressions
Problem 63E
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Given a sequence x₁, x2,... of real numbers, show that
cos(x₁) + + cos(xn)
exists if and only if
exists.
lim
81x
lim
n→∞
n
cos(x₁) + cos(x4) + ... + cos(x²)
n²
Transcribed Image Text:Given a sequence x₁, x2,... of real numbers, show that cos(x₁) + + cos(xn) exists if and only if exists. lim 81x lim n→∞ n cos(x₁) + cos(x4) + ... + cos(x²) n²
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