Absolute convergence, and the absolute convergence test 

Absolute convergence, definition

Let $\sum _{n=m}^{\mathrm{\infty }}{a}_n$ be a formal series of real numbers. The series is said to be absolutely convergent if the series [...] is [...].

In order to distinguish convergence from absolute convergence, we sometimes refer to the former as [...] convergence.

Absolute convergence test

Let $\sum _{n=m}^{\mathrm{\infty }}{a}_n$ be a formal series of real numbers. If the series is [...], then it is also [...]. Furthermore, in this case we have the triangle inequality

Note that the converse of this proposition is not true; there exists series that are conditionally convergent but are not absolutely convergent.