Math 122 - Exam 6 (11.2 - 11.7)

1. Classify the sequence as eventually increasing or eventually decreasing. 3 parts.
1. Use the difference of two consecutive terms
2. Use the ratio of two consecutive terms
3. Use the first derivative test
2. Find the sum of the infinite geometric series. 1 part.
3. Classify each series as absolutely convergent, conditionally convergent, or divergent. Give a justification in each part. Your justification can be informal (it looks like a p-series with p > 1). 10 parts.
4. Identify the convergence or divergence test best described. There is some statement made which is unique to one of the tests. Each test is only used once. Know the divergence test, p-series test, integral test, comparison test, ratio test, root test, limit comparison test, alternating series test, ratio test for absolute convergence (no, the answers aren't in that order). 8 parts.

Notes:

• NO CALCULATORS!
• All problems for questions 1, 2, and 3 are directly from the text and are (as far as I know) even.
• Problems 1, 2, and 3 are 6 points for each part (84 points)
• Problem 4 is 2 points per part (16 points)
• In problem 1, four of the six points are for correctly identifying the sequence as increasing or decreasing. The other two points are for using the correct technique.
• In problem 3, four of the six points are for identifying the convergence or divergence correctly. The other two points are for providing a correct justification.
• You may use note cards with the convergence tests written on them. Each note card may only contain one test and may not contain any worked out examples. It may contain the notes about the usage of the test.