|1/4-1/2|+|1/6-1/4|+|1/8-1/6|+```+|1/2008-1/2006|

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 21:07:23
|1/4-1/2|+|1/6-1/4|+|1/8-1/6|+```+|1/2008-1/2006|

|1/4-1/2|+|1/6-1/4|+|1/8-1/6|+```+|1/2008-1/2006|
|1/4-1/2|+|1/6-1/4|+|1/8-1/6|+```+|1/2008-1/2006|

|1/4-1/2|+|1/6-1/4|+|1/8-1/6|+```+|1/2008-1/2006|
|1/4-1/2|+|1/6-1/4|+|1/8-1/6|+```+|1/2008-1/2006|
=1/2-1/4+1/4-1/6+1/6-1/8+...+1/2006-1/2008
=1/2-1/2008
=1003/2008.

|1/4-1/2|+|1/6-1/4|+|1/8-1/6|+```+|1/2008-1/2006|
=1/2-1/4+1/4-1/6+1/6-……+1/2006-1/2008
=1/2-1/2008
=1003/2008

由于都加了绝对值的 那么去掉绝对值就是1\2-1\4+1\4-1\6....+1\2006-1\2008 把中间的全消掉 只剩第一和最后 结果就是1\2-1\2008=1003\2008

答案:1/2-1/2008=1003/2008
去绝对值得(1/2-1/4)+(1/4-1/6)+(1/6-1/8)+```+(1/2006-1/2008)=1/2-1/2008=1003/2008

1/2-1/4+1/4-1/6+1/6-1/4+.....+1/2006-1/2008= 中间的约掉