 1/2 − 1/4 + 1/8 − 1/16 + ⋯

In mathematics, the infinite series is a simple example of an alternating series that converges absolutely.It is a geometric series whose first term is and whose common ratio is −, so its sum is

A slight rearrangement of the series reads

The series has the form of a positive integer plus a series containing every negative power of two with either a positive or negative sign, so it can be translated into the infinite blue-red Hackenbush string that represents the surreal number