(1)1/1*2*3+1/2*3*4……+1/1993*1994*1995

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/09 03:54:34

(1)1/1*2*3+1/2*3*4……+1/1993*1994*1995
(1)1/1*2*3+1/2*3*4……+1/1993*1994*1995

(1)1/1*2*3+1/2*3*4……+1/1993*1994*1995
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……+1/1993*1994*1995
=1/2*(1/1*2-1/2*3)+1/2(1/2*3-1/3*4)+……+1/2(1/1993*1994-1/1994*1995)
=1/2*(1/1*2-1/2*3+1/2*3-1/3*4+……+1/1993*1994-1/1994*1995)
=1/2*(1/1*2-1/1994*1995)
=1/2*(1/2-1/3978030)
=994507/3978030