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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  .

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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.

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