# The Ratio Test

Let's start by writing out the absolute ratios:

As in the previous example, we can simplify .

For the first term we want to use the hint, so let's rewrite

Do you feel like visiting our Algebra section? Just kidding...

Having jumped this hurdle, we can compute the limit of the ratios as

Thus the radius of convergence is , the series will converge in the interval from to .

Seeing is believing? Here are the pictures of the first terms of the power series:

 Click here if the animation does not work.

Draw the graph of the power series on its interval of convergence. The behavior at the left is different from the behavior at the right. Try to explain the different behaviors!

#### Where to go next?

Go to the Taylor series pages.

Helmut Knaust
Fri Jul 12 16:21:45 MDT 1996
This module consists of 7 HTML pages.

Copyright © 1999-2019 MathMedics, LLC. All rights reserved.
Contact us
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA
users online during the last hour