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Limit Comparison Test (a). Suppose that E ak and Ebk are series with positive terms. If ak lim = c, 0

Limit Comparison Test (a). Suppose that E ak and Ebk are series with positive terms. If ak lim = c, 0

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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Limit Comparison Test (a). Suppose that Eak and Ebk are series with positive terms. If lim = c, 0 <c<∞, k→∞ bk then either both series converge or both diverge. In other words, E=1 bk converges if and only if E=1 ak converges. Using this inter- pretation, give an alternative proof via Cauchy sequences.
Transcribed Image Text:Limit Comparison Test (a). Suppose that Eak and Ebk are series with positive terms. If lim = c, 0 <c<∞, k→∞ bk then either both series converge or both diverge. In other words, E=1 bk converges if and only if E=1 ak converges. Using this inter- pretation, give an alternative proof via Cauchy sequences.
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