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In mathematical analysis, Cesàro summation assigns values to some infinite sums that are not convergent in the usual sense, while coinciding with the standard sum if they are convergent. The Cesàro sum is defined as the limit of the arithmetic mean of the partial sums of the series. Cesàro summation is named for the Italian analyst Ernesto Cesàro (1859–1906). == Definition == Let be a sequence, and let : be the ''k''th partial sum of the series : The series is called Cesàro summable, with Cesàro sum , if the average value of its partial sums tends to : : In other words, the Cesàro sum of an infinite series is the limit of the arithmetic mean (average) of the first ''n'' partial sums of the series, as ''n'' goes to infinity. It is easy to show that any convergent series is Cesàro summable, and the sum of the series agrees with its Cesàro sum. However, as the first example below demonstrates, there are series that diverge but are nonetheless Cesàro summable. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Cesàro summation」の詳細全文を読む スポンサード リンク
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