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 Series Tests for determining convergence/divergence for any infinite series.
In this lecture we’ll explore the first of the 9 infinite series tests – The Nth Term Test, which is also called the Divergence Test.
Test for Divergence
This test, according to Wikipedia, is one of the easiest tests to apply; hence it is the first “test” we 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 series. The steps are identical, but the outcomes are different!
So it is imperative that you make sure that you are aware of whether or not you are dealing with a sequence or a series, because your conclusion of convergence or divergence depends on it.
But don’t worry; it’s easy to sort out, and easy to apply!
In fact, this is probably everyone’s favorite test because it’s so easy to use.
Nth Term Test Video
Nth Term Test
Nth Term Test – 3 Examples
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