Conditional Convergence:n is conditionally convergent ifThe seriesRatio/Root Test:Root: LRatio: LΣThe seriesan converges ifThe series an diverges if:Test inconclusive ifFor each of the following series, argue convergence or divergence using the indicated test.1. 5- cos2(n) (Comparison Test)COsn=1(-1)"n!a(Alternating Series Test)2.n 2n!(Ratio Test)100n=13.

Question
Asked Nov 21, 2019
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For each of the following, fill in the blanks to complete the description of the test.

Conditional Convergence:
n is conditionally convergent if
The series
Ratio/Root Test:
Root: L
Ratio: L
Σ
The series
an converges if
The series an diverges if:
Test inconclusive if
For each of the following series, argue convergence or divergence using the indicated test.
1. 5- cos2(n) (Comparison Test)
COs
n=1
(-1)"
n!
a(Alternating Series Test)
2.
n 2
n!
(Ratio Test)
100
n=1
3.
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Conditional Convergence: n is conditionally convergent if The series Ratio/Root Test: Root: L Ratio: L Σ The series an converges if The series an diverges if: Test inconclusive if For each of the following series, argue convergence or divergence using the indicated test. 1. 5- cos2(n) (Comparison Test) COs n=1 (-1)" n! a(Alternating Series Test) 2. n 2 n! (Ratio Test) 100 n=1 3.

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Expert Answer

Step 1

Conditional convergence:

isconditionally convergent if :
The series
lima existsis a finitenumber but a, =
n 0
n-0
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isconditionally convergent if : The series lima existsis a finitenumber but a, = n 0 n-0

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Step 2

Root test:

Ratio L lim
n+1
The seriesa, converges if L<1
* The series a, diverges if L >1
*Test inconclusive if L = 1
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Ratio L lim n+1 The seriesa, converges if L<1 * The series a, diverges if L >1 *Test inconclusive if L = 1

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Step 3

Root tes...

Ratio L lima
- lim a
*The series a, converges if L <1
*The seriesa diverges if L>1
*Test inconclusive if L 1
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Ratio L lima - lim a *The series a, converges if L <1 *The seriesa diverges if L>1 *Test inconclusive if L 1

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