For a refresher:

A series is the sum of a list of terms that are generated with a pattern. A series is denoted with a summation symbol. An infinite series is a series that has an infinite number of terms being added together.

Here is an example of an infinite series:

In this blog post, I will go over the convergence test for geometric series, a type of infinite series.

A geometric series is a series that has a constant ratio between successive terms. A visualization of this will help you better understand.

Here’s a geometric series:

We can rewrite this geometric series using the summation notation.

If the series is of the form ,

if |r|<1, then the geometric series converges to

if |r|≥1, then the geometric series diverges

Let’s see some examples to better understand.

First example (click here):

The geometric series converges to .

Next example (click here):

2. Determine the value of r

The geometric series diverges.

Last example (click here):

1. Reference the geometric series convergence test

2. Determine the value of r

The geometric series converges to 6.

As you can see, it is not too difficult to determine if a geometric series converges or not. After doing some practice problems, you’ll get the hang of it very quickly. For more help or practice on geometric series, check out Symbolab’s Practice. Next blog post, I’ll go over the convergence test for p-series.

Until next time,

Leah