Category: Assignment Instructions (Page 4 of 8)

Group post due Sunday, April 4

HOT topic Standards 7 and 8 sound almost identical:

7. Determine whether an infinite series converges absolutely, converges conditionally, or diverges

8. Determine whether an infinite series converges or diverges

You’ll be able to tell which of your HOT topics portfolio questions correspond to these standards just by reading the instructions, but that won’t give you much of a hint for how to answer these questions.

For these standards, you may need to apply any of the convergence tests you’re learning in Lessons 14 to 18 on the course hub. You’re learning how to use each these convergence tests one by one over the next few weeks by completing your Rederly homework. Once you’ve mastered a particular convergence test, then you can see if it can be used to answer the Standard 7 or Standard 8 question in your HOT topics portfolio. If that test can’t be used to answer the question, you’ll have to learn how to use a different test to see if it can be applied.

For this group assignment, you’ll get your hands dirty by practicing using the four of these convergence tests on your Rederly homework problems.

Before you meet with your group

1. From the appropriate course hub lessons, copy down the statements of the following four convergence tests:
   1. Integral test
   2. Divergence test
   3. (Direct) comparison test
   4. Limit comparison test
2. Now look at a few questions from each of the corresponding Rederly homework sets (not your HOT topic portfolio):
   1. Series – Integral Test
   2. Series – Divergence Test
   3. Series – Comparison Tests (this covers both the direct and limit comparison tests).
3. For each of the four convergence tests listed above, choose one question from your Rederly homework that looks like it might involve a straightforward application of the test. Bring these four questions to your group.

When you meet with your group

1. As a group, read the statement of the integral test together. Does the integral test make you think of? What questions do you have about it?
2. Each group member will share their Rederly question that might involve a straightforward application of the integral test. As a group, choose the question that appears to be the most straightforward.
3. As a group, work through an answer to the question involving the integral test. Designate a group member who is responsible for writing up the complete solution.
4. Repeat steps 1 to 3 for the divergence test, for the (direct) comparison test, and for the limit comparison test.
5. What are some hints you can use to tell which test will be appropriate for different series? Write a short guide explaining what hints you discovered by working on these examples. Your guide may include bullet points like “If the series looks like …. , then use the … test” (where you fill in the blanks).

Note: some students struggle when they first see any convergence tests (especially the comparison tests) so don’t worry if your group can’t finish during the Wednesday study group session; you have until the end of spring break to submit your post.

Group post instructions

The secretary will need to collect the different group members’ written work files (probably JPGs) to share in the group post.

• Title: Week 8 group n post (where n is your group number)
• Category: Week 8 group post
• Include names of group members who were present.
• Add the group members’ written solutions. Indicate clearly which convergence test is being used for which question and include the statement of the convergence test (you may include a screenshot of the test from the course hub if you like).
• Include the short guide your group wrote with hints about when to use which convergence test.

Comment due Sunday, March 28 (but late comments are okay!)

I’ve been really enjoying getting to know each of you during your HOT topics presentations. Even if we only talk about math and the course, I love getting a little window into how you think.

I know it’s hard getting to know your classmates in an online class; this is one of the reasons that study groups play such a huge role in the class. It’s always extremely helpful to work with other people—doing math can be a really a social activity—and I strongly encourage you to work with your group on homework and HOT topic preparation outside of official group assignments.

Over the past week or so, I’ve introduced a few students to other students who are not in their group (actually, in one case they were in the same group). This is sort of like matchmaking, but it’s not romantic! I’m just trying to pair people whom I think would work well together. Sometimes this is because I think their ways of thinking are similar but sometimes this is because I think their ways of thinking might complement each other. I’m not an expert! It’s just about the vibe get.

So I’d like to open up my study-buddy matchmaking services to the class. Would you like to be matched with a study buddy in the class? If so, please say so in a comment below (or if you’d like to ask privately instead, send me an email with the subject line MAT 1575 matchmaker).

Once you’re matched with a partner, it will be up to you to decide how you’d like to work together. One suggestion is that you set up a time to talk in real time over the weekend about your Rederly homework. Which questions were you each able to answer easily? Which ones stumped you? Can you help your partner to understand something you already understand? If there’s something neither of you understand, can you bounce some relevant ideas back and forth?

You will receive participation credit for requesting a match.