> For the complete documentation index, see [llms.txt](https://solomons-mathbook.gitbook.io/calculus-basics/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://solomons-mathbook.gitbook.io/calculus-basics/comment-399637419/comment-399657906/comment-399949602.md).

# Root Test

"The root test is used in situations where a series term or part of it is **raised to the power of the index variable**. "

> Notice: The root test **isn't** a good choice if a series contains **factorial** terms. If the root test isn't fairly easy to use, you probably **shouldn't** use it. But when it works, it often cuts to convergence or divergence quickly.

[▼Refer to xaktly: Ratio test / root test](http://www.xaktly.com/RatioTestRootTest.html)

![image](https://user-images.githubusercontent.com/14041622/41898160-d147e8c6-795b-11e8-9e9e-5c53918286a7.png)

## Example

![image](https://user-images.githubusercontent.com/14041622/41898303-45560054-795c-11e8-888f-67984ce1b423.png) Solve:

* Apply the `root test`:

  ![image](https://user-images.githubusercontent.com/14041622/41898382-78ae9678-795c-11e8-86d0-6a7d8df23fc6.png)
* Since `L < 1`, so it converges.