# Series

# Geometric Series

If arithmetic series are the burgers of restaurant menus, then geometric series are the hotdogs of restaurant menus. They aren't sold in *every* restaurant, but we all reminisce about our 6-year-old days when we bite into a diner dog.

It would be neat if a geometric series was made from adding up circles, pentagons, and Pac-Man shaped polygons called nomnomagons. But they are much simpler. A **geometric series** is a series whose terms form a geometric sequence.

### Sample Problem

The series

is a geometric series because

is a geometric sequence.

### Sample Problem

The series

is not a geometric series because its terms do not comprise a geometric sequence.

There are two magic formulas we need to know, and know really well, for dealing with geometric series:

- the formula for the sum of a finite geometric series

- the formula for the sum of an infinite geometric series.

A finite geometric series is the same thing as a partial sum of an infinite geometric series. This means, if we can sum finite geometric series, we'll be able to find partial sums of infinite geometric series.