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Consider the series E an, and denote by b. = a4k-3+a4k-2+a4k-1+ a4k for k > 1. Assume that an >0 for all n, and E bk is convergent. Prove that E. and E an =Ex=1 bk• An is convergent

Consider the series E an, and denote by b. = a4k-3+a4k-2+a4k-1+ a4k for k > 1. Assume that an >0 for all n, and E bk is convergent. Prove that E. and E an =Ex=1 bk• An is convergent

Advanced Engineering Mathematics
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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Consider the series E, an, and denote by br = a4k–3+a4k–2+a4k-1+a4k for n=1 k > 1. Assume that an >0 for all n, and E br is convergent. Prove that E, am is convergent n=1 and En-1 an Σ α Σ bμ n=1 k=1
Transcribed Image Text:Consider the series E, an, and denote by br = a4k–3+a4k–2+a4k-1+a4k for n=1 k > 1. Assume that an >0 for all n, and E br is convergent. Prove that E, am is convergent n=1 and En-1 an Σ α Σ bμ n=1 k=1
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