1/(2x4)+1/(4x6)+.+1/(2012x2014) =1/2(1/2-1/4)+1/2(1/4-1/6)+.+1/2(1/2012-1/2014） =1/2[(1/2-1/4)+(1/4-1/6)+.+(1/2012-1/2014）] =1/2(1/2-1/4+1/4-1/6+.+1/2012-1/2014) =1/2(1/2-1/2014) =1/2*1006/2014 =503...