S=1+2x+3x^2+…+ nx^n-1
xS= x+2x^2+3x^3+…+(n-1)x^(n-1)+nx^n
上述两式对应相减,得
(x-1)S=-(1+x+x^2+x^3+……+x^(n-1))+nx^n
(x-1)S=(x^n-1)/(x-1)+nx^n
S=(x^n-1)/((x-1)^2) + (nx^n)/(x-1)