乘以x,再逐项求导：
xs(x)＝∑x^(n+1)/(n+1)
(xs(x))'＝∑x^n＝1/(1-x)
积分,xs(x)＝-ln(1-x)
x≠0时,s(x)＝-ln(1-x)/x.x=0时.s(0)=1
所以s(x)＝
-ln(1-x)/x,x≠0
1,x=0
乘以x,再逐项求导：
xs(x)＝∑x^(n+1)/(n+1)
(xs(x))'＝∑x^n＝1/(1-x)
积分,xs(x)＝-ln(1-x)
x≠0时,s(x)＝-ln(1-x)/x.x=0时.s(0)=1
所以s(x)＝
-ln(1-x)/x,x≠0
1,x=0