Definition:Series/Number Field

Definition
Let $S$ be one of the standard number fields $\Q$, $\R$, or $\C$.

Let $\left \langle {a_n} \right \rangle$ be a sequence in $S$.

A series is what results when $\left \langle {a_n} \right \rangle$ is summed to infinity:
 * $\displaystyle \sum_{n \mathop = 1}^\infty a_n = a_1 + a_2 + a_3 + \cdots$