xSn=x^2+2x^3+…nx^(n+1) 与Sn=x+2x^2+3x^3+…nx^n相减等于多少_数学解答

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

人气：482 ℃　时间：2020-05-15 22:39:47

解答

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)