november 1st, 2007

November 1st, 2007

Welcome toThe Candy Carnival

Quiz 4 ReviewQuiz 4 Review

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

Hide and Seq (100)

Find the rule for the nth term:

€

−2

3,

4

15, −

8

75,

16

375, ...

Hide and Seq (200)

Find the rule for the nth term:

€

3

2,

5

4,

7

6,

9

8,...

Hide and Seq (300)

Determine whether the sequence converges or diverges.

€

lnn

n

⎧ ⎨ ⎩

⎫ ⎬ ⎭n=1

∞

Hide and Seq (400)

Determine whether the sequence converges or diverges.

€

sin1

n

⎛

⎝ ⎜

⎞

⎠ ⎟

⎧ ⎨ ⎩

⎫ ⎬ ⎭n=1

∞

Serial Killers (100)

Find the sum of the series or show that it diverges.

€

(−6)n

52nn=1

∞

∑

Serial Killers (200)

Determine whether the series converges or diverges.

€

n

n2 +1n=1

∞

∑

DAILY DOUBLE

Serial Killers (300)

Find the sum of the series or show that it diverges

€

1

2−

2

3+

3

4−

4

5+L

Serial Killers (400)

Find the sum of the series or show that it diverges.

€

2n − 3n

5nn=0

∞

∑

Your Call (100)

Give an example of a convergent sequence.

Your Call (200)

Give an example of a geometric series that does not converge.

DAILY DOUBLE

Your Call (300)

Give an example of a divergent series whose terms converge to 0.

Your Call (400)

Find a function f(x) such that

is undefined BUT

€

limx→∞

f (x)

€

f (n){ }n=1

∞converges.

Potpourri (100)

Find a geometric series whose sum equals

€

0.17

Find the first four partial sums of the series, then determine the sum of the series.

€

1

n(n+1)n=1

∞

∑

Potpourri (200)

Potpourri (300)

Find the next number in the sequence.

4, 8, 15, 16, 23, …

Potpourri (400)

Determine the values of x for which the series converges.

€

−3

x

⎛

⎝ ⎜

⎞

⎠ ⎟

n=1

∞

∑n

FINAL JEOPARDY

Draw a picture showing that

€

1

nn=1

∞

∑ >1

xdx

1

∞

∫