Definition:Series/Tail

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