Nth Term Test For Divergence

In our previous lesson, Intro To Sequences and Series, we learned important terms such as convergence, divergence, and sequence and series.

We also learned how to:

Generate a sequence
Simplify factorials
Determine convergence for an infinite sequence

We also learned our Important Acronym and Mnemonic Device for the Nine Infinite Serial Tests for determining convergence/divergence for whatsoever infinite serial.

In this lecture we'll explore the outset of the 9 infinite series tests – The Nth Term Test, which is also called the Difference Test.

how to test for divergence of a series

Test for Divergence

This test, according to Wikipedia, is one of the easiest tests to utilize; hence it is the first "test" nosotros bank check when trying to determine whether a series converges or diverges.

What is important to point out is that there is an nth-term test for sequences and an nth-term test for serial. The steps are identical, but the outcomes are different!

Then it is imperative that you lot make sure that you are aware of whether or non y'all are dealing with a sequence or a series, because your conclusion of convergence or divergence depends on it.

But don't worry; it'southward easy to sort out, and piece of cake to apply!

In fact, this is probably everyone's favorite test because it's and then easy to utilise.