L23 Series Summary - Lecture 23 Series Summary It would not...

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Lecture 23: Series SummaryIt would not be wise to apply tests for convergencein a speci c order tond one thatnally works.Instead, a proper stretegy, as with integration, isto classify the series according to its form. Keepin mind that a conclusion about the convergenceof a series sometimes can be reached in di erentways.1.’easier cases’:If a series is of the form ofpseries, 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 ’easiercases’, then one of the comparison tests shouldbe considered. For instance, ifanis a rational oralgebraic expression (contains roots of polynomi-als), then the series should be compaired with apseries.3. It is always easier to see if the necessary con-dition for convergence is met than to check if the1
series is convergent. If liman6= 0, then the series

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