2乘4分之3加4乘6分之3加.2010乘2012分之3
问题描述：
2乘4分之3加4乘6分之3加.2010乘2012分之3
答
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