Uma hierarquia de testes de convergência de séries baseada no teorema de Kummer

In this study we use Kummer’s theorem on convergence of numericalpositive series in order to construct a hierarchy of specific tests, starting from the well-known simple criteria with a less range of application, and reaching more sophisticated results with a wider abrangency. We construct various examples, which illustrate the use of such tests, and analyze situations when all the tests of the presented hierarchy are not conclusive with respect to behavior of a series.