∵∑[n=1,+∞]x^(n+1)=x^2/(1-x) |x|<1∴∑[n=1,+∞](n+1)x^n=[2x(1-x)+x^2]/(1-x)^2=(2x-x^2)/(1-x)^2∑[n=1,+∞]n(n+1)x^(n-1)=[(2-2x)(1-x)^2+2(2x-x^2)(1-x)/(1-x)^4 =2[(1-x)^2+(2x-x^2)](1-x)/(1-x)^4 =2/(1-x)^3
