 The sequence of partial sums clearly shows that the series does not converge to a particular number (for any proposed limit "x", we can find a point beyond which the subsequent partial sums are all outside the interval ["x"−1, "x"+1]), so diverges.Since the terms 1, −2, 3, −4, 5, −6, ... follow a simple pattern, the series can be manipulated by shifting and term-by-term addition to yield a numerical value.If it can make sense to write for some ordinary number "s", the following manipulations argue for 

Although 1 − 2 + 3 − 4 + ... does not have a sum in the usual sense, the equation can be supported as the most natural answer if such a sum is to be defined.