Recap: The convergence of an infinite series depends on the individual terms getting small (going to zero) as we go out further and further in the series, and ALSO on the terms getting small "fast"; i.e., going to zero fast enough that each subsequent term doesn't add too much to the overall sum.
The terms in a Geometric Series get small fast as long as the absolute value of the common ratio is less than 1.
The Ratio Test: Here we will leverage the concept of the Geometric Series to develop a test that uses ratios of terms to determine whether a series converges "absolutely" or not. "Absolute" convergence just means we don't care about the terms changing signs. We'll explore the issue of flip-flopping signs on the terms (Alternating Series) in the next section.
Videos:
Assigned Problems from Textbook
Note: This is a scaled-down set of homework problems as compared to the original assignment sheet.
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1st Edition Section, page 688 9, 10, 11, 13, 15, 16, 17, 84, 87 3rd Edition Section, page 699 9, 10, 13, 15, 21, 22, 60, 63 |