A generalized definition of the "sum" of a divergent series is called a summation method or summability method. There are many different methods (some of which are described below) and it is desirable that they share certain properties with ordinary summation. What the above manipulations actually prove is the following: Given any summability method that is linear and stable and sums the series 1 − 2 + 3 − 4 + ..., the sum it produces is ​1⁄4.[4] Furthermore, since