The Root Test - Calculus 2

One more method we can use to test for the convergence or divergence of a series is what is known as the Root Test. This test will be particularly useful for series that involve powers of n.

The Root Test involves evaluating the limit of the nth root of the absolute value of the nth term of a series. Depending on the value of this limit, L,  we will be able to make one of three conclusions about a given series. The series will either be absolutely convergent (L < 1), divergent (L > 1 or ∞), or the test will be inconclusive (L = 1). When we reach an inconclusive result, we will need to resort to another previously learned test in order to determine if the series converges or diverges. We discuss all this in greater detail in this new lesson. So let's get to it!

In this lesson, you will learn:

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

I hope you find this video to be helpful!

-Josh