 The Cauchy product of two infinite series is defined even when both of them are divergent.In the case where "a""n" = "b""n" = (−1)"n", the terms of the Cauchy product are given by the finite diagonal sums

The product series is then

Thus a summation method that respects the Cauchy product of two series — and assigns to the series the sum 1/2 — will also assign to the series the sum 1/4.With the result of the previous section, this implies an equivalence between summability of and with methods that are linear, stable, and respect the Cauchy product.