1/1*3+1/3*5+1/5*7+1/7*9……1/2007*2009

原式=1/2*(1-1/3+1/3-1/5+...+1/2007-1/2009)
=1/2*(1-1/2009)=1/2*2008/2009
=1004/2009
裂项求和法

=1/2(2/1*3+2/3*5.........2/2007*2009)
=1/2(1-1/3 + 1/3-1/5........+1/2007-1/2009)
=1/2(1-1/2009)
=1004/2009

1/2*(1-1/3+1/3-1/5+1/5.....+1/2007-1/2009)
化简=1/2*(1-1/2009)
=1004/2009