floppy人名:求数列前n项和

来源：百度文库编辑：杭州交通信息网时间：2024/05/09 20:10:30

求
1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+.....+1/(n*(n+1)*(n+2))
表达式~~~~
要证明哦

1/(n*(n+1)*(n+2))
=1/2*[1/(n*(n+1)) -1/((n+1)*(n+2))]

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

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