An Etymological Dictionary of Astronomy and Astrophysics

A series with infinitely many terms, in other words a series that has no last term, such as 1 + 1/4 + 1/9 + 1/16 + · · · + 1/n² + … .

The idea of infinite series is familiar from decimal expansions, for instance the expansion π = 3.14159265358979… can be written as π = 3 + 1/10 + 4/10² + 1/10³ + 5/10⁴ + 9/10⁵ + 2/10⁶ + 6/10⁷ + 5/10⁸ + 3/10⁹ + 5/10¹⁰ + 8/10¹¹ + … , so π is an “infinite sum” of fractions. See also → finite series.

See also: → infinite; → series.