Introduction to the Divergence and Integral Tests

In the previous section, we determined the convergence or divergence of several series by explicitly calculating the limit of the sequence of partial sums [latex]\left\{{S}_{k}\right\}[/latex]. In practice, explicitly calculating this limit can be difficult or impossible. Luckily, several tests exist that allow us to determine convergence or divergence for many types of series. In this section, we discuss two of these tests: the divergence test and the integral test. We will examine several other tests in the rest of this module and then summarize how and when to use them.