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

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/12 09:56:54
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

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
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

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

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

=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5………………-1/2009
=1-1/2009
=2009/2009

结果是2008/2009

1/2-1<0,所以|1/2-1|=-(1/2-1)=1-1/2
同理
1/3-1/2<0,|1/3-1/2|=1/2-1/3
……
|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