p-Series

Return to the Series, Convergence, andSeries Tests starting pageReturn to the List of Common SeriesA series such asis called a p-series. In general, a p-series follows thefollowing form:p-series are useful because of the following theorem:The p-series is convergent ifp > 1and divergent otherwise.Unfortunately, there is no simple theorem to give us thesum of a p-series. For instance, the sum of the example series is.If p=1, we call the resulting series theharmonic series:By the above theorem, the harmonic series does not converge.Return to the Series, Convergence, andSeries Tests starting pageReturn to the List of Common SeriesCopyright © 1996 Departmentof Mathematics, Oregon State UniversityIf you have questions or comments, don't hestitate tocontact us.