上海木材报关公司:数的规律!!!!!!!

来源:百度文库 编辑:杭州交通信息网 时间:2024/05/07 02:03:03
求1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+...+1/(n(n+1)(n+2))的值.

1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+...+1/(n(n+1)(n+2))
=[1/(1*2)-1/(2*3)]/2+[1/(2*3)-1/(3*4)]/2+...+[1/n(n+1)-1/(n+1)(n+2)]/2
={1/(1*2)-1/[(n+1)(n+2)]}/2
=n(n+3)/[4(n+1)(n+2)]