1/(2x4)=1/2(1/2-1/4) 1/(4x6)=1/2(1/4-1/6) 其余的同理
所以原式=1/2(1/2-1/4+1/4-1/6+1/6-1/8.+1/2010-1/2012)
=1/2(1/2-1/2012)
=1005/4024