Remainders

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After completing this section, students should be able to do the following.

Understand why bounds for remainders are necessary.
Approximate the value of a series that converges by the alternating series test.
Approximate the value of a series that converges by the integral test.
Estimate the value of a convergent series by a term in the sequence of partial sums.
Understand when a better approximation can be produced by using the sequence of partial sums and error bounds.