原式=1/2(1/2-1/4)+1/2(1/4-1/6)+…+1/2(1/2006-1/2008)=1/2(1/2-1/4+1/4-1/6+1/6-…+1/2006-1/2008)=1/2(1/2-1/2008)=1003/4016