infinite series

== English == === Noun === infinite series (plural infinite series) (mathematical analysis) Any expression that represents the addition a countably infinite number of ordered summands, often explicitly indexed by the positive or nonnegative integers. ==== Usage notes ==== 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 ====