I need your help!1 1 1 1 1--- + --- + --- + .+ --------- + ------_数学解答

I need your help!
1 1 1 1 1
--- + --- + --- + .+ --------- + ---------
1*3 3*5 5*7 2001*2003 2003*2005
=
=
=
=

人气：212 ℃　时间：2020-03-04 11:34:42

解答

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