Definition:Series/Tail

Definition
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 $\displaystyle \sum_{n \mathop =1}^\infty a_n$.