Pries M161: Rock the test! Review sheet for Chapter 11
Chapter 11 is the most important material in the calculus curriculum. Try making flashcards!
Definitions What is the technical definition of each topic? What does it mean? Why is
it useful? What major theorems are there for this topic? What is an example of each topic?
1. Series and partial sums
2. Convergence/divergence of series
3. Absolute/conditional convergence
4. Power series
5. Radius and interval of convergence
6. Taylor/Maclaurin series
7. Error for Taylor polynomials
Tests for convergence For each test write down: i) what the test says;
ii) a short explanation of why it is true;
iii) an example of a series which converges by this test;
iv) an example of a series which diverges by this test;
v) how this test can be used to approximate the sum of a series;
vi) what information this test gives you about the error for partial sums.
(There will not be an answer to every question for every test.)
1. Test for divergence
2. Integral test
3. Comparison test
4. Limit comparison test
5. Ratio test
6. Root test
7. Alternating series test
Important examples Find a classic example of each of the following types. Does it
converge? Which test did we use? How can you find or approximate the sum?
1. Geometric series
2. Telescoping series
3. Harmonic series
4. Alternating harmonic series
5. p-series
6. Frequently used Taylor series (pg 831)
Practice exercises: pg 840-842 19,23,27,31,33,41,47,51,53,55,59,61,67,73,77,79,85,