# Science:Infinite Series Module/Appendices/The Contrapositive and the Divergence Test

## Introduction

The divergence test is based on the following result that we were able to prove:

If the series
is convergent, then the limit
equals zero. |

We claimed that it is equivalent to this statement (which is the divergence test):

If the limit
is not zero, then the series
is not convergent. |

Let's look at this more closely to see why this would be the case. We will use the concept of the **contrapositive**.

## Topics

- Definition of the Contrapositive
- A Few Contrapositive Examples
- A Closer Look at the Contrapositive with Sets