|1-1/2|+|1/3-1/2|+|1/4-1/3|+.+|1/1000-1/999|
来源：学生作业帮助网 编辑：六六作业网 时间：2024/12/23 18:55:54
|1-1/2|+|1/3-1/2|+|1/4-1/3|+.+|1/1000-1/999||1-1/2|+|1/3-1/2|+|1/4-1/3|+.+|1/1000-1/999||1-1/2|+|1/3
|1-1/2|+|1/3-1/2|+|1/4-1/3|+.+|1/1000-1/999|
|1-1/2|+|1/3-1/2|+|1/4-1/3|+.+|1/1000-1/999|
|1-1/2|+|1/3-1/2|+|1/4-1/3|+.+|1/1000-1/999|
1-1/2=1-1/2
|1/3-1/2|=1/2-1/3
...
|1/1000-1/999|=1/999-1/1000
所以原式
=1-1/2+1/2-1/3+.+1/999-1/1000=1-1/1000=999/1000