Math 141, Spring 2016, Assignment 9

Mathematical proofs, like diamonds, are hard as well as clear, and will be touched with nothing but strict reasoning.

- John Locke, Second Reply to the Bishop of Worcester

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

1. Sequence.
2. Limit of a sequence.
3. Convergent sequence.
4. Divergent sequence.
5. Series.
6. Sequence of terms associated with a series.
7. Sequence of partial sums associated with a series.
8. Sum of a series.
9. Convergent series.
10. Divergent series.

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

1. Polar arc length formula.
2. Polar area formula.

Solve the following problems:

1. Section 9.5, problems 5, 13, 17, 19, and 25.
2. Section 8.1, problems 5, 7, 9, 11, 17, 19, 21, 23, 25, 27, 29, 31, 33, and 35.

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