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

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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.


  1. Definition of the Contrapositive
  2. A Few Contrapositive Examples
  3. A Closer Look at the Contrapositive with Sets