来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/11 15:24:50
I need your help!
1 1 1 1 1
--- + --- + --- + .+ --------- + ---------
1*3 3*5 5*7 2001*2003 2003*2005
=
=
=
=
1/1*3+1/3*5+1/5*7+…+1/2003*2005
=1/2(2/1*3+2/3*5++…+2/2003*2005 )
＝1/2(1-1/3+1/3-1/5+1/5-1/7+...+1/2003-1/2005)
=1/2(1-1/2005)
=1002/2005
作业帮