求幂级数 ∑(n=1,∝) x^n/[n(n+1)] 的和函数

f(x)=∑x^n/[n(n+1)]求导：f'(x)=∑ x^(n-1)/(n+1)F=x^2f'(x)= ∑ x^(n+1)/(n+1)再求导：F'=∑ x^n=x/(1-x)=1/(1-x)-1积分：F=-ln(1-x)-xf'(x)=F/x^2=-ln(1-x)/x^2-1/x再积分：f(x)=ln(1-x)/x+∫x/(1-x)dx-lnx=ln(1-x)/x-ln(1-x)-x-lnx=[ln(1-x)]/x-ln[x(1-x)]-x