Question

这道数学题怎么做 |�0�5-1|+|1/3-1/2|+|1/4-1/3|+.......+|1/20-1/19|

这道数学题怎么做
|�0�5-1|+|1/3-1/2|+|1/4-1/3|+.......+|1/20-1/19|算法也要必须的求急啊！！！！！简单点说我是个初一新生

Answer 1

首先去绝对值符号
原式等价于（1-(1/2)）+((1/2)-(1/3))+((1/3)-(1/4))+....+((1/19)-(1/20))
=1-(1/2)+(1/2)-(1/3)+(1/3)-(1/4)+.....+(1/19)-(1/20)
(规律：每个括号里面的后一项与下一个括号里面的前一项抵消)
=1-(1/20)=(19/20)

Answer 2

|�0�5-1|+|1/3-1/2|+|1/4-1/3|+.......+|1/20-1/19|
=1-1/2+1/2-1/3+1/3-1/3-4+.......+1/19-1/20
=1-1/20
=19/20

Answer 3

1/2+1/3+1/4+1/5…1/19=19/20