解:1/1*2+1/2*3+1/3*4+……+1/2008*2009 =1-1/2+1/2-1/3+1/3-1/4++1/2008-1/2009 =1-1/2009 =2008/2009 祝你开心
1×1/2+1/2×1/3+1/3×1/4+1/4×1/5+1/5×1/6+1/6×1/7=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7=1-1/7=6/7
