 Cesàro's theorem is a subtle example.The series is Cesàro-summable in the weakest sense, called while requires a stronger form of Cesàro's theorem, being Since all forms of Cesàro's theorem are linear and stable, the values of the sums are as we have calculated.To find the (C, 1) Cesàro sum of 1 − 2 + 3 − 4 + ..., if it exists, one needs to compute the arithmetic means of the partial sums of the series.