What is the alternating series test?

In this section we will learn about what alternating series are. It is very easy to see if the series is alternating by expanding it out. If the terms go from positive to negative and negative to positive, then it is alternating. We will also examine the convergence of alternating series by using a method called the alternating series test. The test requires two conditions, which is listed below. Keep in mind that if you cannot fulfill these conditions, that does not mean the alternating series is divergent. There is still a possibility that it is convergent.Alternating Series TestThe alternating series test (also known as the Leibniz test), is type of series test used to determine the convergence of series that alternate. Keep in mind that the test does not tell whether the series diverges. In order to use this test, we first need to know what a converging series and a diverging series is.What is a convergent series? What is a divergent series? A convergent series is an infinite serie...