Limit Comparison Test (LCT):c=Case 1: cSOCase 2: cSOCase 3: cSOAlternating Series Test (AST):The series-1)bn converges if:For convergent alternating series, we know that s-,Absolute Convergence:The seriesan is absolutely convergent ifConditional Convergence:The seriesan is conditionally comvergent ifRatio/Root Test:Ratio: LRoot: 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!2.2n!(Ratio Test)1003.VI

Question
Asked Nov 20, 2019
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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
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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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Expert Answer

Step 1

Since we only answer up to 3 sub-parts, we’ll answer the first 3.

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Step 2

Limit Comparison test-

Assume,

c lim
n
baPositive term series
a Positive term series
2
Case1-If c 0, then a, and b both converge or both diverge.
Case 2-If c 0 and b, is convergent, then >a, is convergent
Case 3-If c and b, is divergent, then a, is divergent
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c lim n baPositive term series a Positive term series 2 Case1-If c 0, then a, and b both converge or both diverge. Case 2-If c 0 and b, is convergent, then >a, is convergent Case 3-If c and b, is divergent, then a, is divergent

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Step 3

Alternating series test-

1)The ...

b
Σ-1
-1
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b Σ-1 -1

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