The Z transformation has many applications in Mathematics, especially in solving difference equations to help handle discrete data models. This article provides one more application of the Z transformation, which is the summation of a series. The author through the research method of theory development from some properties of the Z transformation to obtain the result which is a theorem about the formula for the sum of a series, with the proof attached. From there, apply the theorem together with the Z transformation to calculate the sum of some series in specific problems. Thus, the problem of calculating the sum of the series has one more method of solving, as well as expanding the application of the Z transformation in the field of Mathematics, especially analysis.