Definition:Series/Tail
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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.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): remainder: 2.