Question

初一数学问题 |1/2-1|+|1/3-1/2|+|1/4-1/3|+.……|1/20-1/19|

大家很积极，请说明原理

Answer 1

因为每一个绝对值中的数相减都为负，所以去掉绝对值要在前面加负号，最终为
(-1/2)+1-(1/3)+(1/2)-(1/4)+(1/3)......(-1/20)+(1/19)=1-(1/20)=19/20

Answer 2

|1/2-1|+|1/3-1/2|+|1/4-1/3|+.……|1/20-1/19|
=1-1/2+1/2-1/3+1/3-1/4+……+1/19-1/20
=1-1/20
=19/20

Answer 3

原式=1-1/2+1/2-1/3+……+1/19-1/20=1-1/20=19/20

Answer 4

解：
|1/2-1|+|1/3-1/2|+|1/4-1/3|+……|1/20-1/19|
=（1-1/2）+（1/2-1/3）+（1/3-1/4）+……+（1/19-1/20）
=1-1/20
=19/20

Answer 5

19/20

Answer 6

19/20