November 1st, 2007 Welcome to The Candy Carnival.
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Transcript of November 1st, 2007 Welcome to The Candy Carnival.
![Page 1: November 1st, 2007 Welcome to The Candy Carnival.](https://reader035.fdocuments.us/reader035/viewer/2022062806/5697bf921a28abf838c8f1cd/html5/thumbnails/1.jpg)
November 1st, 2007
Welcome toThe Candy Carnival
![Page 2: November 1st, 2007 Welcome to The Candy Carnival.](https://reader035.fdocuments.us/reader035/viewer/2022062806/5697bf921a28abf838c8f1cd/html5/thumbnails/2.jpg)
Quiz 4 ReviewQuiz 4 Review
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JEOPARDYHide and
SeqSerial Killers
Your Call Potpourri
100 100 100 100
200 200 200 200
300 300 300 300
400 400 400 400
FINAL JEOPARDY
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Hide and Seq (100)
Find the rule for the nth term:
€
−2
3,
4
15, −
8
75,
16
375, ...
![Page 5: November 1st, 2007 Welcome to The Candy Carnival.](https://reader035.fdocuments.us/reader035/viewer/2022062806/5697bf921a28abf838c8f1cd/html5/thumbnails/5.jpg)
Hide and Seq (200)
Find the rule for the nth term:
€
3
2,
5
4,
7
6,
9
8,...
![Page 6: November 1st, 2007 Welcome to The Candy Carnival.](https://reader035.fdocuments.us/reader035/viewer/2022062806/5697bf921a28abf838c8f1cd/html5/thumbnails/6.jpg)
Hide and Seq (300)
Determine whether the sequence converges or diverges.
€
lnn
n
⎧ ⎨ ⎩
⎫ ⎬ ⎭n=1
∞
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Hide and Seq (400)
Determine whether the sequence converges or diverges.
€
sin1
n
⎛
⎝ ⎜
⎞
⎠ ⎟
⎧ ⎨ ⎩
⎫ ⎬ ⎭n=1
∞
![Page 8: November 1st, 2007 Welcome to The Candy Carnival.](https://reader035.fdocuments.us/reader035/viewer/2022062806/5697bf921a28abf838c8f1cd/html5/thumbnails/8.jpg)
Serial Killers (100)
Find the sum of the series or show that it diverges.
€
(−6)n
52nn=1
∞
∑
![Page 9: November 1st, 2007 Welcome to The Candy Carnival.](https://reader035.fdocuments.us/reader035/viewer/2022062806/5697bf921a28abf838c8f1cd/html5/thumbnails/9.jpg)
Serial Killers (200)
Determine whether the series converges or diverges.
€
n
n2 +1n=1
∞
∑
![Page 10: November 1st, 2007 Welcome to The Candy Carnival.](https://reader035.fdocuments.us/reader035/viewer/2022062806/5697bf921a28abf838c8f1cd/html5/thumbnails/10.jpg)
DAILY DOUBLE
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Serial Killers (300)
Find the sum of the series or show that it diverges
€
1
2−
2
3+
3
4−
4
5+L
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Serial Killers (400)
Find the sum of the series or show that it diverges.
€
2n − 3n
5nn=0
∞
∑
![Page 13: November 1st, 2007 Welcome to The Candy Carnival.](https://reader035.fdocuments.us/reader035/viewer/2022062806/5697bf921a28abf838c8f1cd/html5/thumbnails/13.jpg)
Your Call (100)
Give an example of a convergent sequence.
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Your Call (200)
Give an example of a geometric series that does not converge.
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DAILY DOUBLE
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Your Call (300)
Give an example of a divergent series whose terms converge to 0.
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Your Call (400)
Find a function f(x) such that
is undefined BUT
€
limx→∞
f (x)
€
f (n){ }n=1
∞converges.
![Page 18: November 1st, 2007 Welcome to The Candy Carnival.](https://reader035.fdocuments.us/reader035/viewer/2022062806/5697bf921a28abf838c8f1cd/html5/thumbnails/18.jpg)
Potpourri (100)
Find a geometric series whose sum equals
€
0.17
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Find the first four partial sums of the series, then determine the sum of the series.
€
1
n(n+1)n=1
∞
∑
Potpourri (200)
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Potpourri (300)
Find the next number in the sequence.
4, 8, 15, 16, 23, …
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Potpourri (400)
Determine the values of x for which the series converges.
€
−3
x
⎛
⎝ ⎜
⎞
⎠ ⎟
n=1
∞
∑n
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FINAL JEOPARDY
Draw a picture showing that
€
1
nn=1
∞
∑ >1
xdx
1
∞
∫