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.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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8. For two sequences {an} and {b,}, let c,n =
E arbn-k. (Then cn is the
sum of the terms on the nth diagonal in the picture on page 453.) The
series Cn is called the Cauchy product of E
an and b,. If an = bn
%3D
n=1
n=1
n-1
(-1)"Vn, show that c 2 1, so that the Cauchy product does not
converge.
Transcribed Image Text:8. For two sequences {an} and {b,}, let c,n = E arbn-k. (Then cn is the sum of the terms on the nth diagonal in the picture on page 453.) The series Cn is called the Cauchy product of E an and b,. If an = bn %3D n=1 n=1 n-1 (-1)"Vn, show that c 2 1, so that the Cauchy product does not converge.
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