# Definition:Series/Tail

Let $\left({S, \circ}\right)$ be a semigroup.
Let $\left \langle {a_n} \right \rangle$ be a sequence in $S$.
Let $N \in \N$.
The expression $\displaystyle \sum_{n \mathop = N}^\infty a_n$ is known as a tail of the series $\displaystyle \sum_{n \mathop = 1}^\infty a_n$.