求和1xX+2xX^2+3xX^3+…+nxX^n.

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求和1xX+2xX^2+3xX^3+…+nxX^n.

求和1xX+2xX^2+3xX^3+…+nxX^n.
求和1xX+2xX^2+3xX^3+…+nxX^n.

求和1xX+2xX^2+3xX^3+…+nxX^n.
原式=Sn
X*Sn=1xX^2+2xX^3+…+nxX^(n+1)=Sn+1-(X+X^2+X^3+…+X^n+X^n+1)
Sn+1-X*Sn=(X-X^n+2)/(1-X)
Sn+1=Sn+(n+1)xX^n+1
(1-X)Sn=(X-X^n+2)/(1-X)-(n+1)xX^n+1
Sn=[X-(n+1)xX^n+1+nxX^n+2]/(1-X)^2