Math 141, Spring 2016, Assignment 12

Algebra begins with the unknown and ends with the unknowable.

- Anonymous

Carefully define the following terms, then give one example and one non-example of each:

1. Absolutely convergent (series).
2. Conditionally convergent (series).
3. Power series centered at $x=c$.

Carefully state the following theorems (you do not need to prove them):

1. Theorem relating absolute convergence to convergence.
2. Theorem concerning the dependence of a sum on the order in which the terms are taken.
3. Alternating series test.
4. Error bound for alternating series.

Solve the following problems:

1. Section 8.5, problems 5, 7, 9, 11, 13, 15, 17, 19, 25, and 27.
2. Section 8.2, problems 37 and 39.

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