Suppose Σ Xk converges absolutely, and that Σ xk = L k=1 k=1 (a) Prove that Σ/(k=1k||4|. Note: this is short, but don't simply assume that lim∞ |Σk=1xk| = | limn→∞ Σ^k=1×k| · no
Suppose Σ Xk converges absolutely, and that Σ xk = L k=1 k=1 (a) Prove that Σ/(k=1k||4|. Note: this is short, but don't simply assume that lim∞ |Σk=1xk| = | limn→∞ Σ^k=1×k| · no
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![Suppose Σ Xk converges absolutely, and that Σ Xk
=
= L
k=1
k=1
(a) Prove that Σ^/(±1×k| → |4|. Note: this is short, but don't simply assume that
limn→∞ | Σkk±1×k| = | limn→∞ Σk=1×k| ·](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe92a9736-6814-4c32-a8c8-4e39e2246344%2F5f3d5d67-d451-42b1-989d-ac49864d4f5e%2Fjjsry6_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose Σ Xk converges absolutely, and that Σ Xk
=
= L
k=1
k=1
(a) Prove that Σ^/(±1×k| → |4|. Note: this is short, but don't simply assume that
limn→∞ | Σkk±1×k| = | limn→∞ Σk=1×k| ·
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