用高中导数求和：Sn=1+2x+3x2+.+nx(n-1)

把Sn看作f(x)则F(x)=∫f(x)dx=x+x^2+x^3+...+x^n+C=(x-x^(n+1))/(1-x)+C所以f(x)=F'(x)=[(1-(n+1)x^n)(1-x)-(x-x^(n+1))(-1)]/(1-x)^2=(1-x-(n+1)x^n+(n+1)x^(n+1)+x-x^(n+1))/(1-x)^2=(1-(n+1)x^n+nx^(n+1))/(1-x)^...