xSn=x^2+2x^3+…nx^(n+1) 与Sn=x+2x^2+3x^3+…nx^n相减 等于多少

xSn-Sn
=(x^2+2x^3+…nx^(n+1))-(x+2x^2+3x^3+…nx^n
)
=-x-x^2-x^3-..-x^n+nx^(n+1)
=-x(x^(n+1)-1)/(x-1)+nx^(n+1)

xSn-Sn=nx^(n+1) -(x+x^2+x^3+…x^n)
=nx^(n+1) -[x^(n+1)-x]/(x-1)