THEOREM 10.15 Limit Comparison Test Let Ea, and Eb, be series with positive terms and let lim L. 1. If 0 < L < ∞ (that is, L is a finite positive number), then Ea, and Eb, either both converge or both diverge. 2. If L = 0 and Eb, converges, then Ea, converges. 3. If L = ∞ and Eb, diverges, then Ea, diverges. VR + 1 ,2 =1 Vk + 2
THEOREM 10.15 Limit Comparison Test Let Ea, and Eb, be series with positive terms and let lim L. 1. If 0 < L < ∞ (that is, L is a finite positive number), then Ea, and Eb, either both converge or both diverge. 2. If L = 0 and Eb, converges, then Ea, converges. 3. If L = ∞ and Eb, diverges, then Ea, diverges. VR + 1 ,2 =1 Vk + 2
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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Use the Comparison Test or the Limit Comparison Test to determine whether the following series converge.
Transcribed Image Text:THEOREM 10.15 Limit Comparison Test
Let Ea, and Eb, be series with positive terms and let
lim
L.
1. If 0 < L < ∞ (that is, L is a finite positive number), then Ea, and Eb,
either both converge or both diverge.
2. If L = 0 and Eb, converges, then Ea, converges.
3. If L = ∞ and Eb, diverges, then Ea, diverges.
Transcribed Image Text:VR + 1
,2
=1 Vk + 2
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