What is "convergent series"

n. (context analysis English) An infinite series whose partial sums converge

In mathematics, a series is the sum of the terms of an infinite sequence of numbers.

Given an infinite sequence (a,  a,  a, …), the nth partial sum S is the sum of the first n terms of the sequence, that is,

S = ∑a.

A series is convergent if the sequence of its partial sums {S,  S,  S, …} tends to a limit; that means that the partial sums become closer and closer to a given number when the number of their terms increases. More precisely, a series converges, if there exists a number ℓ such that for any arbitrarily small positive number ɛ, there is a (sufficiently large) integer N such that for all n ≥  N,

∣S − ℓ| ≤  ɛ.
If the series is convergent, the number ℓ (necessarily unique) is called the sum of the series.

Any series that is not convergent is said to be divergent.

Convergent Series is a collection of science fiction and fantasy short stories by Larry Niven, published in 1979. It is also the name of one of the short stories in the collection. The collection reprints the stories originally appearing in the 1969 collection The Shape of Space that were not part of the Known Space series (The Known Space stories were previously reprinted in 1975's Tales of Known Space and 1976's The Long ARM of Gil Hamilton). The collection includes newer stories, both fantasy and sf, some of which are in the Draco's Tavern series, none of which are in the Known Space series.