Please solve 8. For two sequences {an} and {b,}, let c,n =E arbn-k. (Then cn is thesum of the terms on the nth diagonal in the picture on page 453.) Theseries Cn is called the Cauchy product of Ean and b,. If an = bn%3Dn=1n=1n-1(-1)"Vn, show that c 2 1, so that the Cauchy product does notconverge.

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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

Section10.1: Infinite Sequences And Summation Notation

Problem 72E

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