│1/2-1│+│1/3-1/2│+│1/4-1/3│+...+│1/2007-1/2006│=? 

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/17 09:26:26
│1/2-1│+│1/3-1/2│+│1/4-1/3│+...+│1/2007-1/2006│=? │1/2-1│+│1/3-1/2│+│1/4-1/3│+...+│1/2007-1/200

│1/2-1│+│1/3-1/2│+│1/4-1/3│+...+│1/2007-1/2006│=? 
│1/2-1│+│1/3-1/2│+│1/4-1/3│+...+│1/2007-1/2006│=?
 

│1/2-1│+│1/3-1/2│+│1/4-1/3│+...+│1/2007-1/2006│=? 
|1/2-1|+|1/3-1/2|+|1/4-1/3|+...+|1/2007-1/2006|=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2006-1/2007)=1-1/2007=2006/2007

很简单,
原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2005-1/2006)+(1/2006-1/2007)=1-1/2007=2006/2007