请各位老师帮我!1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6).+1/(2007×2

1/(1×2)=1/1-1/2
1/(2×3)=1/2-1/3
1/(3×4)=1/3-1/4
...
...
...
1/(2007×2008）=1/2007-1/2008
所以和为
原式
1-1/2008 中间全部抵消
=2007/2008