# Divergence test

##### Intros

##### Examples

###### Free to Join!

StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun — with achievements, customizable avatars, and awards to keep you motivated.

#### Easily See Your Progress

We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.#### Make Use of Our Learning Aids

#### Earn Achievements as You Learn

Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.#### Create and Customize Your Avatar

Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.

###### Topic Notes

In this lesson, we will learn about the divergence test. The test states that if you take the limit of the general term of the series and it does not equal to 0, then the series diverge. Keep in mind that if you do take the limit and it goes to 0, that does not mean the series is convergent. It only means the test has failed, and you will have to use another method to find the convergence or divergence of the series. It is recommended to use the divergence test if u can obviously see that the limit of the general term goes to infinity. For the first few questions, we will see if the divergence test applies to the series. For the last question, we will see if the series is convergent or divergent by using the test.

Note *The divergence test states the following:

If $\lim$

If $\lim$

_{n →$\infty$}$a$_{$n$}$\neq$ 0, then the series $\sum a_n$ diverges.2

videos

remaining today

remaining today

5

practice questions

remaining today

remaining today