1*2*3+2*3*4...........n*(n+1)*(n+2) 用求和公式杂求??

n*(n+1)*(n+2)
=n³+3n²+2n

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