已知：an=n(n+1)(n+2) 求：Sn

n(n+1)(n+2) =3!*C(n+2,3)
Sn=3!*[ C(3,3)+C(4,3)+C(5,3)+……+C(n+2,3)]
=3!*C(n+3,4)
=3!(n+3)!/4!(n-1)!
=(n+3)(n+2)(n+1)n/4

An=n(n+1)(n+2)=n(n^2+3n+2)=n^3+3n^2+2n

设An1=n^3 所以,Sn1=[n(1+n)/2]^2
设An2=3n^2 所以,Sn2=3*[n(n+1)(2n+1)/6]=n(n+1)(2n+1)/2
设An3=2n 所以,Sn3=n(2n+2)/2=n(n+1)
所以,An=An1+An2+An3=[n(1+n)/2]^2+n(n+1)(2n+1)/2+n(n+1)
就告诉你这些了 化简的事你自己来吧 呵呵