Imagine you have a secret. You tell 3 friends, who each tell 3 friends, who then tell another 3 friends. This is an example of a geometric series.
Geometric Series: 1 + 3 + 9 + 27, r = 3
Here's an example of an Infinite Geometric Series:
Each term is half of its previous term, and the series continues forever. How do we find the sum of a series that continues forever?
|Sum of an Infinite Geometric Series|
The sum of an infinite geometric series is found using the equation:
when -1 < r < 1
First, we determine r by dividing any term by the term just before it:
Now that we have r, we can calculate our sum:
Our infinite geometric series sums to 1.
The sum of an infinite geometric series only exists if -1 < r < 1.
An infinite geometric series that has a sum is called a convergent series.