dots

Represents horizontal ellipsis (a sequence of dots) to indicate continuation of a pattern or series in mathematical expressions.

Overview

Essential for concisely representing mathematical sequences, series, and patterns without writing every term explicitly. Particularly valuable in:

Summations and products with multiple terms
Matrix notation to indicate omitted elements
Number sequences where the pattern is clear
Mathematical induction proofs
Computer science and programming contexts for representing array indices

Often preferred over repeated writing of terms when the pattern is obvious to readers, helping maintain clean and readable mathematical expressions while preserving mathematical rigor.

Examples

Sequence of numbered variables in a sum

x_1 + \dots + x_n

x_1 + \dots + x_n

Matrix elements along the main diagonal

a_{11}, \dots, a_{nn}

a_{11}, \dots, a_{nn}

Series expansion with higher-order terms

f(x) = 1 + x + \frac{x^2}{2!} + \dots + \frac{x^n}{n!}

f(x) = 1 + x + \frac{x^2}{2!} + \dots + \frac{x^n}{n!}