An Etymological Dictionary of Astronomy and Astrophysics
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A sum a₁ + a₂ + a₃ + · · · + a_N, where the a_i's are real numbers. In terms of Σ-notation, it is written as a₁ + a₂ + a₃ + · · · + a_N = Σ (n = 1 to N).  See also → infinite series.

→ finite; → series.

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.

→ infinite; → series.