=1/2（1/2-1/4）+1/2（1/4-1/6）+...1/2（1/2008-1/2010）
=1/2(1/2-1/4+1/4-1/6+...+1/2008-1/2010)
=1/2(1/2-1/2010)
=1/2*1004/2010
=502/2010
=251/1005