In mathematical analysis, Cesaro summation is an alternative means of assigning a sum to an infinite series. If the series converges in the usual sense to a sum A, then the series is also Cesaro summable and has Cesaro sum A. The significance of Cesaro summation is that a series which does not converge may still have a well-defined Cesaro sum. However, a series which positively diverges to an infinite value, will not be summable to a finite value in any case. Cesaro summation is named for the Italian analyst Ernesto Cesaro (1859–1906).

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