化简:|1/2-1|+|1/3-1/2|+|1/4-1/3|+……+|1/2010-1/2009|

来源:学生作业学帮网 编辑:学帮网 时间:2024/06/17 22:07:46

化简:|1/2-1|+|1/3-1/2|+|1/4-1/3|+……+|1/2010-1/2009|

原式=1-1/2+1/2-1/3+……+1/2009-1/2010
=1-1/2010
=2009/2010

|1/2-1|+|1/3-1/2|+|1/4-1/3|+……+|1/2010-1/2009|
1-1/2+1/2-1/3+1/3-1/4+...+1/2009-1/2010
=1-1/2010=2009/2010