2/1X2+2/2X3+2/3X4+……+2/2007X2008等于多少（需要过程）急!
问题描述：
2/1X2+2/2X3+2/3X4+……+2/2007X2008等于多少（需要过程）急!
急..
答
2/1X2+2/2X3+2/3X4+……+2/2007X2008 =2X[(2-1)/1X2+(3-2)2/2X3+(4-3)/3X4+……+(2008-2007)/2007X2008] =2X(1-1/2+1/2-1/3+1/3-1/4+……+1/2007-1/2008] =2x(1-1/2008)=2*2007/2008=2007/1004