november 20th, 2007
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November 20th, 2007. Happy T-Day to You. Quiz 5 Review. JEOPARDY. FINAL JEOPARDY. Integration Nation (100). Test for convergence:. Integration Nation (200). Test for convergence:. Integration Nation (300). - PowerPoint PPT PresentationTRANSCRIPT
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November 20th, 2007
Happy T-Day to You
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Quiz 5 ReviewQuiz 5 Review
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JEOPARDYIntegration Nation
Gettin’ Some R&R
Beyond Compare
Potpourri
100 100 100 100200 200 200 200300 300 300 300400 400 400 400
FINAL JEOPARDY
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Integration Nation (100)
Test for convergence:
€
1
n lnnn=2
∞
∑
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Integration Nation (200)
Test for convergence:
€
ne−n2
n=1
∞
∑
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Integration Nation (300)
Is the integral test an appropriate test for determining the convergence of the alternating harmonic series? Explain.
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Integration Nation (400)
How many terms in the series
would you need to add to find its sum to within 0.01?
€
1
n2n=1
∞
∑
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Gettin' Some R&R (100)
Test for convergence:
€
n3n
4nn=1
∞
∑
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Gettin' Some R&R (200)
What can you say about the series an in each of the following cases?
€
limn→∞
an+1an
=3
4
€
limn→∞
an+1an
=4
3
€
limn→∞
an+1an
=1
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DAILY DOUBLE
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Gettin' Some R&R (300)
Test the series for convergence:
€
n!
enn=1
∞
∑
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Gettin' Some R&R (400)
Test the series for convergence:
€
( 2n −1)n
n=1
∞
∑
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Beyond Compare (100)
Test the series for convergence:
€
1+sinn
n nn=1
∞
∑
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Beyond Compare (200)
Test the series for convergence.
€
n2.2 −n0.3
n3.1 +n0.2n=1
∞
∑
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DAILY DOUBLE
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Beyond Compare (300)
Test the series for convergence.
€
3n
4n + 7n=1
∞
∑
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Beyond Compare (400)
Suppose bn is a series with positive terms.
T or F: (justify your answer)
• If an < bn for all n and bn converges, an is a convergent series
• If an > bn for all n and bn diverges, an is a divergent series.
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Potpourri (100)
Find a geometric series whose sum equals
€
0.17
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Test the series for convergence.
€
2n
n2n=1
∞
∑
Potpourri (200)
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Potpourri (300)
Test the series for convergence:
€
(−n)n
n2nn=1
∞
∑
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Potpourri (400)
Determine the values of p for which the series converges.
€
1
n(lnn)pn=2
∞
∑
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FINAL JEOPARDY
Directions: write as much information as you can about the following series.
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€
1.(−1)n
nn=1
∞
∑
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€
2.3n+1
22nn=1
∞
∑
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€
3.1
n(n+1)n=1
∞
∑
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€
4.(−1)n
nn=1
∞
∑
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€
5.en
n!n=1
∞
∑
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€
6. sinnn=1
∞
∑
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€
7. n−0.7
n=1
∞
∑
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€
8. (−1)n sin(1/n)n=1
∞
∑
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€
9.n!
(n+1)!n=1
∞
∑
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€
10. (−1)n
n=1
∞
∑