At a Glance - 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.
is a geometric series because
is a geometric sequence.
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.