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. 1 + cos? k k – 3 k=4

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
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Use the Comparison Test or the Limit Comparison Test to determine whether the following series converge.

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: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.
1 + cos? k
k – 3
k=4
Transcribed Image Text:1 + cos? k k – 3 k=4
Expert Solution
Step 1

Given series k=41+cos2kk-3.

Here ak=1+cos2k,bk=k-3.

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