1/2*4+1/4*6+1/6*8+1/8*10+1/10*12.....+1/2010*2012=1/2*(1/2-1/4+1/4-1/6+...+1/2010-1/2012)=1/2*(1/2-1/2012)=1/2*1005/2012=1005/4024
