- The harmonic series is divergent.
- The alternating harmonic series is convergent.
- A geometric series is convergent if, and only if .
- The Riemann series is convergent if, and only if .

The converse is not true: for example, the alternating harmonic series is convergent, but not absolutely convergent, thus it is conditionally convergent.

A convergent series which is convergent, but not absolutely convergent is conditionally convergent.

Noah Dana-Picard 2007-12-24