Group Presentation

Chapter 11 - 35 points

There are eight tests for convergence that we are going to study in chapter 11. The instructor presented two of the tests, you get to present the other six.

There are nine people in the class and only six tests, so three of you will get to work alone and the other six will have to work in pairs. Pick one of the tests. For that test, do the following.

- Present the material for that test to the class.
- You may use any method, lecture, handout, group discussion, etc that you wish to.
- You must do at least two examples using that technique. These problems may be from the homework problems. Be sure to show each possible outcome from the test. That is, if the test can indicated convergence or divergence, then be sure you show at least one example that converges and one that diverges.
- Explain when the best time to use that technique is. Explain when it doesn't work and if you have time, show an example of why it doesn't work.
- Be able to answer any questions on the technique.
- Assign three even problems that require the use of the technique.
- These may not be the problems that you worked as examples.
- Try to spread the problems around so that all outcomes are used.
- Collect and grade the problems from the rest of the students. Each problem is worth 1 point and is either right or wrong.
- You are allowed to help the other classmates with their homework, but you are not allowed to give them the answer.
- Your grade will be based on the following criteria
- The presentation is worth 10 points.
- You may get up to 15 points for the three problems assigned for each of the five tests that you didn't present.
- To encourage you to do a good job explaining the topic and helping the other students understand the material, you will be awarded up to ten points based on how well the other students do with your topic. Take the number of points earned divided by the total number of points for your topic and multiply by 10. Example: The other 8 students earned 20 out of 23 on your topic. You get 20/23 * 10 = 8.7 9 points.
- The entire project is worth 35 points.

Points. For each test, record the points you received for that section. For the test that you presented, record the value from part 3c.

_____ Presentation (10 pts)

_____ Comparison Test (11.6)

_____ Ratio Test (11.6)

_____ Root Test (11.6)

_____ Limit Comparison Test (11.6)

_____ Alternating Series Test (11.7)

_____ Ratio Test for Absolute Convergence (11.7)

_____ Total (35 pts)

**Comparison Test**- Bob, Patrick
- 11.6.22: sum(1/(2k+1),k,1,inf)
- 11.6.26: sum(k^2/(k^3+1),k,1,inf)
- 11.6.2b: sum(2/(k^4+k),k,1,inf)
- Due Friday, Nov 2
**Ratio Test**- Paul, Silpa
- 11.6.12
- 11.6.14
- 11.6.16
- Due Friday, Nov 2
**Root Test**- Eric
- 11.6.12
- 11.6.18
- 11.6.20
- Due Friday, Nov 2
**Limit Comparison Test**- Scott
- 11.6.6
- 11.6.8
- 11.6.10
- Due Monday, Nov 5
**Alternating Series Test**- Nathan
- 11.7.2
- 11.7.4
- 11.7.6
- Due Tuesday, Nov 6
**Ratio Test for Absolute Convergence**- Bradley, Stacey
- 11.7.8
- 11.7.12
- 11.7.24
- Due Tuesday, Nov 6