│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:作业帮 时间:2024/04/30 00:32:01
│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│=? 
|1/2-1|+|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