8. For two sequences {an} and {b,}, let cn = E arbn-k. (Then cn is the sum of the terms on the nth diagonal in the picture on page 453.) The series Ž Cn is called the Cauchy product of n-1 a, and Ebn. If a, = b, = %3D カ=1 n=1 (-1)"Vn, show that c 2 1, so that the Cauchy product does not converge.
8. For two sequences {an} and {b,}, let cn = E arbn-k. (Then cn is the sum of the terms on the nth diagonal in the picture on page 453.) The series Ž Cn is called the Cauchy product of n-1 a, and Ebn. If a, = b, = %3D カ=1 n=1 (-1)"Vn, show that c 2 1, so that the Cauchy product does not converge.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 50E
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