The Ratio Test - Calculus 2

Another test for the convergence or divergence of a series that we can use is what is known as the Ratio Test. This test will be particularly useful for series that involve factorials and exponential parts, and not so helpful for series that are similar to a p-series.

The Ratio Test involves evaluating the limit of the ratio between the n+1 and nth terms of a series. Depending on the result of this limit, we can make one of three different conclusions about the series. The series will either be absolutely convergent, divergent, or the test will be inconclusive. In these instances of inconclusiveness, we will need to use another previously learned test to determine the convergence or divergence of the series. And that is all there really is to say about the Ratio Test for series, and so let's get right into the details of the lesson!

In this lesson, you will learn:

• The convergence and divergence rules for the Ratio Test
• How to use the Ratio Test for a given series
• What to do when the Ratio Test is inconclusive

I hope you find this video to be helpful!

-Josh