Question

1*2*3+2*3*4+3*4*5+.+9*10*11=

Answer 1

1×2×3+2×3×4+3×4×5+.+n(n+1)(n+2)

=1/4【1×2×3×4-0×1×2×3】+1/4【2×3×4×5-1×2×3×4】+1/4【3×4×5×6-2×3×4×5】+.+

1/4【n(n+1)(n+2)（n+3)-(n-1)n(n+1)(n+2)】

=1/4n(n+1)(n+2)(n+3)

将n=9代入,得原式=1/4*9*10*11*12=2970