1乘2乘3加2乘3乘4一直加到n乘(n+1)乘(n+2)

Question

1乘2乘3加2乘3乘4一直加到n乘(n+1)乘(n+2)

Answer 1

因为：
n*(n+1)*(n+2)
=n³+3n²+2n
而：
1³+……+n³=n²(n+1)²/4
1²+……+n²=n(n+1)(2n+1)/6
1+……+n=n(n+1)/2
所以原式
=n²(n+1)²/4+3n(n+1)(2n+1)/6+2n(n+1)/2
=n(n+1)(n+2)(n+3)/4