Nth Term Test for Divergence
The nth term test tests for divergence with the following condition:
However, it only tests for divergence. It cannot prove convergence. Therefore,
Choose another test if this happens. This happens because if the terms don’t approach 0, the series will continue growing and growing (diverging).
Examples
Worked Solutions
A more formal justification would require use of L’Hopital’s Rule for the limit, but the above is the essence of the question.
Again, a more formal justification would require the use of L’HR for the limit.
Flipped Math
Flipped Math is an awesome resource with full packets, test prep, and corrective assignments for each lesson!
Math Libretexts
Math LibreTexts is a free online resource packed with textbooks and learning materials for math students. It simplifies complex concepts, provides practice examples, and offers interactive features for convenient learning anytime, anywhere. It’s like a superhero ally for math students, making math easier to understand and excel in.
Paul's Online Notes
Paul’s Online Notes is another amazing resource with in-depth explanations and a few examples. The first part of the article linked below explains geometric series!
Khan Academy
A classic resource for a reason, Khan Academy offers a ton of practice resources with explanatory videos. However, they’re known for being easier than the actual AP test so you might want to supplement with other resources to make sure you’re prepared for test day.