november 20th, 2007

November 20th, 2007

Happy T-Day to You

Quiz 5 ReviewQuiz 5 Review

JEOPARDYIntegration Nation

Gettin’ Some R&R

Beyond Compare

Potpourri

100 100 100 100200 200 200 200300 300 300 300400 400 400 400

FINAL JEOPARDY

Integration Nation (100)

Test for convergence:

€

1

n lnnn=2

∞

∑

Integration Nation (200)

Test for convergence:

€

ne−n2

n=1

∞

∑

Integration Nation (300)

Is the integral test an appropriate test for determining the convergence of the alternating harmonic series? Explain.

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

∞

∑

Gettin' Some R&R (100)

Test for convergence:

€

n3n

4nn=1

∞

∑

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

DAILY DOUBLE

Gettin' Some R&R (300)

Test the series for convergence:

€

n!

enn=1

∞

∑

Gettin' Some R&R (400)

Test the series for convergence:

€

( 2n −1)n

n=1

∞

∑

Beyond Compare (100)

Test the series for convergence:

€

1+sinn

n nn=1

∞

∑

Beyond Compare (200)

Test the series for convergence.

€

n2.2 −n0.3

n3.1 +n0.2n=1

∞

∑

DAILY DOUBLE

Beyond Compare (300)

Test the series for convergence.

€

3n

4n + 7n=1

∞

∑

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.

Potpourri (100)

Find a geometric series whose sum equals

€

0.17

Test the series for convergence.

€

2n

n2n=1

∞

∑

Potpourri (200)

Potpourri (300)

Test the series for convergence:

€

(−n)n

n2nn=1

∞

∑

Potpourri (400)

Determine the values of p for which the series converges.

€

1

n(lnn)pn=2

∞

∑

FINAL JEOPARDY

Directions: write as much information as you can about the following series.

€

1.(−1)n

nn=1

∞

∑

€

2.3n+1

22nn=1

∞

∑

€

3.1

n(n+1)n=1

∞

∑

€

4.(−1)n

nn=1

∞

∑

€

5.en

n!n=1

∞

∑

€

6. sinnn=1

∞

∑

€

7. n−0.7

n=1

∞

∑

€

8. (−1)n sin(1/n)n=1

∞

∑

€

9.n!

(n+1)!n=1

∞

∑

€

10. (−1)n

n=1

∞

∑