计算:|1/2-1|+|1/3-1/2|+|1/4-1/3|+...+|1/2008-1/2007|+|1/2009-1/2008|

问题描述:

计算:|1/2-1|+|1/3-1/2|+|1/4-1/3|+...+|1/2008-1/2007|+|1/2009-1/2008|
rt,不仅说答案,还要讲的够详细,好的追加分

|1/2-1|+|1/3-1/2|+|1/4-1/3|+...+|1/2008-1/2007|+|1/2009-1/2008|
=1-1/2+1/2-1/3+1/3-1/4+.+1/2007-1/2008+1/2008-1/2009
=1-1/2009
=2008/2009