S=∑(n=1到∞)[n(n+1)/2]x^(n-1)积分得：F=∑(n=1到∞)[(n+1)/2]x^n再积分得：G=0.5∑(n=1到∞)x^(n+1)=0.5x^2/(1-x)求导得：F=0.5[2x(1-x)+x^2]/(1-x)^2=0.5(2x-x^2)/(1-x)^2再求导得：S=0.5[(2-2x)(1-x)+2(2x-x^2)...