# Category:Series

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This category contains results about Series.

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

## Subcategories

This category has the following 13 subcategories, out of 13 total.

### A

### C

### D

### H

### L

### M

### P

### S

### T

## Pages in category "Series"

The following 33 pages are in this category, out of 33 total.

### C

- Cauchy Condensation Test
- Cauchy Product of Absolutely Convergent Series
- Comparison Test
- Comparison Test/Corollary
- Convergence of Square of Linear Combination of Sequences whose Squares Converge
- Convergent Sequence with Finite Number of Terms Deleted is Convergent
- Convergent Series of Natural Numbers