原式=½*(1/2-1/4)+½*(1/4-1/6)+½*(1/6-1/8)+...+½*(1/2010-1/2012)=½*(1/2-1/4+1/4-1/6+1/6-1/8+...+1/2010-1/2012)=½*(1/2-1/2012)=½*1005/2012=1005/4024