1/(2*4)+1/(4*6)+1/(6*8)+……+1/(2010*2012)
=(1/2)*[2/(2*4)+2/(4*6)+2/(6*8)+……+2/(2010*2012)]
=(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