1/2*4=1/2*(1/2-1/4),1/4*6=1/2*(1/4-1/6),以此类推得到所求式子=1/2*(1/2-1/4+1/4-1/6+1/6-....-1/2006+1/2006-1/2008)=1/2*(1/2-1/2008)=1003/4016
3166
