因为4(n-1)n(n+1)=(n-1)n(n+1)(n+2)-(n-2)(n-1)n(n+1)所以1*2*3+2*3*4+3*4*5+......+n(n+1)(n+2) =n(n+1)(n+2)(n+3)÷41*2*3+2*3*4+3*4*5+4*5*6+5*6*7+6*7*8+7*8*9=7×8×9×10/4=1260
