# Definition:Series/Tail

## Definition

Let $\struct {S, \circ}$ be a semigroup.

Let $\sequence {a_n}$ be a sequence in $S$.

Let $N \in \N$.

The expression $\ds \sum_{n \mathop = N}^\infty a_n$ is known as a tail of the series $\ds \sum_{n \mathop = 1}^\infty a_n$.

## Also known as

Some sources give this as the remainder, but that word already has a number of uses.