Cesàro summation

In mathematical analysis, Cesàro summation (also known as the Cesàro mean or Cesàro limit) assigns values to some infinite sums that are not necessarily convergent in the usual sense. The Cesàro sum is defined as the limit, as n tends to infinity, of the sequence of arithmetic means of the first n partial sums of the series.

This special case of a matrix summability method is named for the Italian analyst Ernesto Cesàro (1859–1906).

The term summation can be misleading, as some statements and proofs regarding Cesàro summation can be said to implicate the Eilenberg–Mazur swindle. For example, it is commonly applied to Grandi's series with the conclusion that the sum of that series is 1/2.