Question

1×2×3+2×3×4+3×4×5+...8×9×10要步骤

Answer 1

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)÷4

1*2*3+2*3*4+3*4*5+4*5*6+5*6*7+6*7*8+7*8*9+8*9*10

=8×9×10×11/4

=1980