令S=k1+2k2+...+nkn=2*[3^0+2*3^1+3*3^2+………+n*3^(n-1)]-(1+n)n/2令T=3^0+2*3^1+3*3^2+……+n*3^(n-1),则3T=3^1+2*3^2+3*3^3+……+n*3^n,两式相减，得-2T=3^0+3^1+3^2+……+3^(n-1)-n*3^n=(1-3^n)/(1-3)-n*3^n=(1/2)*3^n-1/2-n*3^n,∴T=(-1/4)*3^n+1/4+(1/2)n*3^n,∴S=2T-(1+n)n/2=(-1/2)*3^n+n*3^n+1/2-(1+n)n/2,