L23 Series Summary

L23 Series Summary - Lecture 23: Series Summary It would...

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Lecture 23: Series Summary It would not be wise to apply tests for convergence in a speci±c order to ±nd one that ±nally works. Instead, a proper stretegy, as with integration, is to classify the series according to its form. Keep in mind that a conclusion about the convergence of a series sometimes can be reached in di²erent ways. 1. ’easier cases’: If a series is of the form of p ± series, geometric series or telescoping series, their convergence properties are known. In fact, the de±nite sum of a geometric series or a tele- scoping series can be found if it is convergent. 2. If a series has a form similar to the ’easier cases’, then one of the comparison tests should be considered. For instance, if a n is a rational or algebraic expression (contains roots of polynomi- als), then the series should be compaired with a p ± series. 3. It is always easier to see if the necessary con- dition for convergence is met than to check if the 1
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series is convergent. If lim a n 6 = 0, then the series is divergent by Test for Divergent.
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L23 Series Summary - Lecture 23: Series Summary It would...

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