Category:Definitions/Series

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This category contains definitions related to Series.
Related results can be found in Category:Series.


Let $\left({S, \circ}\right)$ be a semigroup.

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


Informally, a series is what results when an infinite product is taken of $\left \langle {a_n} \right \rangle$:

$\displaystyle s := \sum_{n \mathop = 1}^\infty a_n = a_1 \circ a_2 \circ a_3 \circ \cdots$


Formally, a series is a sequence in $S$.