Limit Comparison Test (LCT): c= Case 1: c SO Case 2: c SO Case 3: c SO Alternating Series Test (AST): The series -1)bn converges if: For convergent alternating series, we know that s-, Absolute Convergence: The seriesan is absolutely convergent if Conditional Convergence: The seriesan is conditionally comvergent if Ratio/Root Test: Ratio: L Root: L= The seriesan converges if: The seriesan diverges if: Test inconclusive if: For each of the following series, argue convergence or divergence using the indicated test. 1. 5Cos(n) (Comparison Test) (1)(Alternating Series Test) n! 2. 2 n! (Ratio Test) 100 3. VI

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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For each of the following, fill in the blanks to complete the description of the test.

Limit Comparison Test (LCT):
c=
Case 1: c
SO
Case 2: c
SO
Case 3: c
SO
Alternating Series Test (AST):
The series
-1)bn converges if:
For convergent alternating series, we know that s-,
Absolute Convergence:
The seriesan is absolutely convergent if
Conditional Convergence:
The seriesan is conditionally comvergent if
Ratio/Root Test:
Ratio: L
Root: L=
The seriesan converges if:
The seriesan diverges if:
Test inconclusive if:
For each of the following series, argue convergence or divergence using the indicated test.
1. 5Cos(n) (Comparison Test)
(1)(Alternating Series Test)
n!
2.
2
n!
(Ratio Test)
100
3.
VI
Transcribed Image Text:Limit Comparison Test (LCT): c= Case 1: c SO Case 2: c SO Case 3: c SO Alternating Series Test (AST): The series -1)bn converges if: For convergent alternating series, we know that s-, Absolute Convergence: The seriesan is absolutely convergent if Conditional Convergence: The seriesan is conditionally comvergent if Ratio/Root Test: Ratio: L Root: L= The seriesan converges if: The seriesan diverges if: Test inconclusive if: For each of the following series, argue convergence or divergence using the indicated test. 1. 5Cos(n) (Comparison Test) (1)(Alternating Series Test) n! 2. 2 n! (Ratio Test) 100 3. VI
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