Definition:Series

Series in a Standard Number Field
The usual context for the definition of a series occurs when $S$ is one of the standard number fields $\Q, \R, \C$.

Notation
When there is no danger of confusion, the limits of the summation are implicit and the notations:


 * $\displaystyle \sum a_n$

and


 * $\displaystyle \sum_n a_n$

are often seen for $\displaystyle \sum_{n \mathop = 1}^\infty a_n$.

Also known as
Some sources use the term infinite series, but the adjective is technically redundant in that series are defined as being infinite.

Also see

 * Definition:Convergent Series
 * Definition:Infinite Product