1/(2*4)=(1/2-1/4)*1/21/(4*6)=(1/4-1/6)*1/2.1/(2006*2008)=(1/2006-1/2008)1/2*4+1/4*6+1/6*8+····+1/2006*2008=1/2*(1/2-1/4+1/4-1/6+...+1/2006-1/2008)=1/2*(1/2-1/2008)=1/2*1003/2008=1003/4016