Question

I need your help!

Answer 1

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