# Ratio Test

**THIS TEST IS GOOD FOR** `FACTORIALS`**.**

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

![image](https://user-images.githubusercontent.com/14041622/41852093-b5fa6214-78bc-11e8-8c7d-0a4e34c40fa5.png)

## Example

![image](https://user-images.githubusercontent.com/14041622/41895543-e1542e02-7954-11e8-90f6-7d8cdcf82e4b.png) Solve:

*   Apply the `ratio test`:

    ![image](https://user-images.githubusercontent.com/14041622/41895582-ff709358-7954-11e8-891f-c495c31c204b.png)
* `L = 0`, so the series absolutely converges.

## Example

![image](https://user-images.githubusercontent.com/14041622/41896356-f7ba714a-7956-11e8-92aa-ec44c734c3a2.png) Solve:

* Apply the `ratio test`, let `a_(n+1) / a_n`.
* The trick is to know: `(n+1)! = (n+1)·n!`, and `(n+8)! = (n+8)·(n+7)!`
*   Take the limit to get:&#x20;

    ![image](https://user-images.githubusercontent.com/14041622/41896515-5e3bb488-7957-11e8-85d3-d55cafb0d33e.png)
* According to the ratio test, if `L = 1`, then there's no conclusion.
