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 $S$.

Then $\left \langle {s_N} \right \rangle$ is the sequence defined as:
 * $\displaystyle s_N = \sum_{n \mathop = 1}^N a_n = a_1 + a_2 + \cdots + a_N$

Then we refer to $\left \langle {s_N} \right \rangle$ as the sequence of partial sums of the series $\displaystyle \sum_{n \mathop = 1}^\infty a_n$.