1X2+2X3+3X4+、、、、、、+nX(n+1)=(1/3)(1*2*3-0*1*2)+(1/3)(2*3*4-1*2*3)+(1/3)(3*4*5-2*3*4)+....+(1/3)[n*(n+1)(n+3)-(n-1)*n*(n+1)]=(1/3)[n(n+1)(n+2)-0]=n(n+1)(n+2)/3