Question

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

Answer 1

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)