1) Cauchy Product For n € N, let and (-1)n an == bn == √n+1 n Cn == =Σan-k · bk. k=0 Show that the series Σa and b converge, but their Cauchy product Σ Cr does not converge.
1) Cauchy Product For n € N, let and (-1)n an == bn == √n+1 n Cn == =Σan-k · bk. k=0 Show that the series Σa and b converge, but their Cauchy product Σ Cr does not converge.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 49RE
Question
Transcribed Image Text:1) Cauchy Product
For n € N, let
and
(-1)n
an ==
bn ==
√n+1
n
Cn ==
=Σan-k · bk.
k=0
Show that the series Σa and b converge, but their Cauchy product Σ Cr does not
converge.
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