Category: Week 10 group post (Page 2 of 2)

Part 1

Credit: Ken Mei

Mahmoud

Mohamed

Omar

Jonathan

Raneem

Due Monday, November 7

In Lessons 13 to 18, you’ll be learning about different tests you can apply to see whether an infinite series converges or diverges. The first few tests appear in Lessons 15 and 16 (some actually appear in Lesson 13 as well). Not all tests can be use on all series, but sometimes more than one test can be applied to a series.

HOT Topics Standards 7 and 8 require you to use convergence/divergence tests to determine whether a given series converges or diverges:

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

Often—especially when you’re first learning about how these tests work—you’ll just have to guess which test to apply when and see what happens. Often, your first guess won’t end up working out. This is good because it will help you learn when to apply which test in the future.

Part 1

As a group, go through Lessons 13 to 15 on the Course Hub and make a list of

• the convergence/divergence tests in these lessons (both the name of the test and how to apply it)
• special types of series where you don’t need a convergence test

Part 2

Each group member will either generate one HOT topics practice set in WeBWorK, or dig out an old HOT topics question sheet. On your set/sheet identify the questions that align with Standards 7 and 8 respectively. As a group, discuss these questions. Can you apply one of your tests/special series from Part 1 to answer any of them?

Choose a question where each of the following tests may be applied (one question per test, four questions total):

1. divergence test
2. integral test
3. comparison test
4. limit comparison test

As a group discuss why you chose a particular test for each question. Write a few sentences describing how you made your your choice (refer to specific details in the series). Then use the test to determine whether the series in each question converges or diverges (four solutions total).

Hint: this will be easier after you have completed the WeBWork sets:

• Series – Integral Test
• Series – Divergence Test
• Series – Comparison Tests

Group post

Share your group’s list from Part 1.

For Part 2, for each of the four questions, the group post will contain the description of the choice of test, as well as the full worked solution for each of the four questions.

• Title: Week 10 group post
• Category: Week 10 group post