 Formally one computes, for each "n", the average σ"n" of the first "n" partial sums, and takes the limit of these Cesàro means as "n" goes to infinity.For Grandi's series, the sequence of arithmetic means is
or, more suggestively,
where
This sequence of arithmetic means converges to 1⁄2, so the Cesàro sum of Σ"a""k" is 1⁄2.Equivalently, one says that the Cesàro limit of the sequence 1, 0, 1, 0, … is 1⁄2.