\begin{definition}[Definition:Series/Sequence of Partial Sums]
Let $\sequence {a_n}$ be a sequence in a structure $S$.
Let $s$ be the the series:
:$\ds s = \sum_{n \mathop = 1}^\infty a_n = a_1 + a_2 + a_3 + \cdots$
The sequence $\sequence {s_N}$ defined as the indexed summation:
:$\ds s_N: = \sum_{n \mathop = 1}^N a_n = a_1 + a_2 + a_3 + \cdots + a_N$
is the '''sequence of partial sums''' of the series $\ds \sum_{n \mathop = 1}^\infty a_n$.
\end{definition}