Calculus II - 9.2.3 The nth Term Test for Divergence

One of the easiest tests to learn and use, assuming we can find the limit as the series approaches infinity!

Video Chapters:
Intro 0:00
Keep Track of What you Know 0:08
What the nth Term Test Tells Us 1:29
Using the nth Term Test for Divergence (3 Examples) 4:24
Up Next 8:14

This playlist follows Larson and Edwards, Calculus 12e.

[gentlemandude]

7:00 - Wait a minute! You are drawing a false conclusion from the test. You can't conclude that example b is convergent by the nth term test simply because the limit of the sequence a_n = 0; that's not how the test works. When the limit of a_n = 0, this particular test is *inconclusive*, which is to say that the series MAY converge, but it may not as well. You can only establish the convergence/divergence of this series by using another test, such as the Integral Test or the Limit Comparison Test. The nth term test has nothing to say about convergence of series; it can only conclusively establish divergence. Recall that there are sequences whose limit = 0, but whose series are in fact divergent (e.g. the harmonic series), it is not possible to generalize the result in way that you have done here. Furthermore, the limit of the series in example b is in fact divergent, not convergent.

[kofiboateng]

In the three examples for the nth term test, each have different starting points for n (n=1 or n=0), however the test states that it starts at n=1, therefore for the first example, wouldnt you have to rework it to get to n=1? It will still converge but I wanted to make sure whether or not rewriting a(n) is applicable to ALL test and not SOME test

[shreyashtiwari]

Your video are very helpful mam...I saw your full playlist of Discrete Mathematics... 👍👍👍

[DiscoPvPMegaWalls]

With all due respect, this video is incorrect, especially as the other comment pointed out.