# Infinite Geometric Series

### Common Formula (Finite & Infinite)

![image](https://user-images.githubusercontent.com/14041622/41807143-89e212a6-76fc-11e8-9d7d-6d3bc7cb80dd.png)

### Infintite Formula

![image](https://user-images.githubusercontent.com/14041622/41807292-9bc31fb2-76ff-11e8-850e-ba958f2a4644.png)

## Determine the Infinite Geometric Series Converges or Diverges

There are two basic rules for infinite **geometric** series: ![image](https://user-images.githubusercontent.com/14041622/41807088-b999b338-76fb-11e8-804d-835f2a3e5a62.png)

### Example

![image](https://user-images.githubusercontent.com/14041622/41807280-57378090-76ff-11e8-8736-4d7a5bb983f7.png) Solve:

* Yes. Because `|-0.8| < 1`, satisfies the basic converge rules.

## Evaluate Infinite Geometric Series

### Example

![image](https://user-images.githubusercontent.com/14041622/41807153-ce600af0-76fc-11e8-85d4-9a85f577cedd.png) Solve:

* First off, we need to find the essential information for the geometric series:
  * Initial term: `a₀ = 1`
  * Common Ratio: `r = 0.75`
*   So the Infinite series would be:

    ![image](https://user-images.githubusercontent.com/14041622/41807199-867cdafa-76fd-11e8-8382-cf206dece606.png)
