1x2=1⼀3x(1x2x3-0x1x2)2x3=1⼀3x(2x3x4-1x2x3)3x4=1⼀3x(3x4x5-2x3x4)求1x2x3+2x3x4+3x4x5+...+7x8x9=?

2024-12-25 14:12:53
推荐回答(1个)
回答1:

一般的,有:
(n-1)n(n+1)
=n^3-n

{n^3}求和公式:Sn=[n(n+1)/2]^2
{n}求和公式:Sn=n(n+1)/2

1x2x3+2x3x4+3x4x5+....+7x8x9
=2^3-2+3^3-3+...+8^3-8
=(2^3+3^3+...+8^3)-(2+3+...+8)
=[(8*9/2)^2-1]-8*9/2+1
=1260