The Series sum from n=1 to ∞(x~n) Applies in Solving Summation Function and Summation of Series

Series is a principal part of mathematics analysis.It widely apply to solution of certain physical problems and production technology.The role of sum from n=1 to ∞(x~n) in solving Summation Function and Summation of Series is discussed in this paper and have given some conclusions which helps solve the problem of Summation of Series.