1/2x4+1/4x6+1/6x8+.+1/2010x2012
=1/2[(1/2-1/4)+(1/4-1/6)+(1/6-1/8)...+[1/2010-1/2012]
=1/2*(1/2-1/2012)
=1/2*1005/2012
=1005/4024