计算 |1/2008-1/2007|+|1/2007-1/2006|+…+|1/2-1|

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/03 23:25:27
计算 |1/2008-1/2007|+|1/2007-1/2006|+…+|1/2-1|

计算 |1/2008-1/2007|+|1/2007-1/2006|+…+|1/2-1|
计算 |1/2008-1/2007|+|1/2007-1/2006|+…+|1/2-1|

计算 |1/2008-1/2007|+|1/2007-1/2006|+…+|1/2-1|
|1/2008-1/2007|+|1/2007-1/2006|+…+|1/2-1|
=1/2007-1/2008+1/2006-1/2007+1/2005-1/2006+…+1-1/2
=-1/2008+1
=2007/2008
对吗?对吧!

原式可等于1/2007-1/2008+1/20061/2007+1/2005+1/2006......+1/2-1/3+1-1/2
绝对值里面的得出的是负数,加上绝对值就是正的等价于后面的减去前面的以此类推的出上面的式子中间的1/2007、1/2006、1/2005........都可以相互消去只剩下-1/2008+1=2007/2008

=1/2007-1/2008+1/2006-1/2007+-----+1-1/2
=1-1/2008
=2007/2008