Category:Convergent Complex Series
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This category contains results about Convergent Complex Series.
Let $S$ be one of the standard number fields $\Q, \R, \C$.
Let $\ds \sum_{n \mathop = 1}^\infty a_n$ be a series in $S$.
Let $\sequence {s_N}$ be the sequence of partial sums of $\ds \sum_{n \mathop = 1}^\infty a_n$.
It follows that $\sequence {s_N}$ can be treated as a sequence in the metric space $S$.
If $s_N \to s$ as $N \to \infty$, the series converges to the sum $s$, and one writes $\ds \sum_{n \mathop = 1}^\infty a_n = s$.
A series is said to be convergent if and only if it converges to some $s$.