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

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

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

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

1/(n*(n+2))=0.5(1/n-1/(n+2))
所以原式
=0.5(1-1/2005)
=1002/2005

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