# Category:Convergent Series

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This category contains results about Convergent Series.

Definitions specific to this category can be found in Definitions/Convergent 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 $s$.

## Subcategories

This category has only the following subcategory.

### E

## Pages in category "Convergent Series"

This category contains only the following page.