Definition. A series is absolutely convergent if the series is convergent.

A series is conditionally convergent if the series is convergent but is not absolutely convergent.

Example.

Theorem. If a series is absolutely convergent then it is convergent.

Discussion [Using Flash] [Using Java]

Exercises:

Corollary. The Absolute Ratio Test.
  1. If then is convergent.

  2. If then is divergent.

Comment. The ratio test gives no information when