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<Ernesto Cesàro> was a <mathematician> whose work included <differential geometry>, <number theory> and divergent <series>. He studied with <Eugène Charles Catalan> and developed the summation method that now bears his name.https://mathshistory.st-andrews.ac.uk/Biographies/Cesaro/[Biography, mathematical training and principal contributions]{ref} <Cesàro summation> replaces the sequence of partial sums of a <series> by their arithmetic averages. For $1-1+1-1+\cdots$, the partial sums alternate between one and zero, but their averages tend to $1/2$. This supplies a generalized sum while preserving the distinction from ordinary <convergence>: the original sequence of partial sums still has no limit.

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Ernesto Cesàro

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