infinite series

Definition from Wiktionary, the free dictionary
Jump to: navigation, search

English[edit]

Noun[edit]

infinite series (plural infinite series)

  1. (analysis) Any expression that represents the addition a countably infinite number of ordered summands, often explicitly indexed by the positive or nonnegative integers.
    In 1734, Leonhard Euler solved the Basel problem by summing the infinite series .

Usage notes[edit]

The sum of an infinite series is formally defined as the limit, if it exists, of the sequence of partial sums of the first n elements as n increases to infinity (i.e., becomes arbitrarily large). If the limit exists, the series is said to be convergent; otherwise it is divergent.

Translations[edit]