1/1×2+1/2×3+1/3×4+……+1/2005×2006+1/2006×2007+1/2007×2008
问题描述：
1/1×2+1/2×3+1/3×4+……+1/2005×2006+1/2006×2007+1/2007×2008
答
1/1×2+1/2×3+1/3×4+……+1/2005×2006+1/2006×2007+1/2007×2008
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2005-1/2006)+(1/2006-1/2007)+(1/2007-1/2008)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2005-1/2006+1/2006-1/2007+1/2007-1/2008
中间抵消
=1-1/2008
=2007/2008