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
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
答
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5………………-1/2009
=1-1/2009
=2009/2009
答
结果是2008/2009
答
1/2-1同理
1/3-1/2……
|1/2009-1/2008|=1/2008-1/2009
所以原式=1-1/2+1/2-1/3+1/3-1/4+……+1/2008-1/2009
=1-1/2009
=2008/2009
答
去||号得
（1-1/2）+（1/2-1/3）.....+(1/2008-1/2009)
前后把+-不同的相同项去除
得1-1/2009=2008/2009
答
|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