Question

初中绝对值问题：|1/20-1/19|+|1/19-1/18|+|1/18-1/17|+......+|1/2-1|

急急急急急急急急急急急急急急急急急急！！！！！！！！

Answer 1

差为负值时，去掉绝对值符号后，减数与被减数互调位置

|1/20-1/19|+|1/19-1/18|+|1/18-1/17|+......+|1/2-1|
=1/19-1/20+1/18-1/19+1/17-1/18+1/16-1/17+.....+1/2-1/3+1-1/2
=-1/20+1
=19/20

Answer 2

=1/19-1/20+1/18-1/19+1/17-1/18+..........+1-1/2= -1/20+1=19/20

Answer 3

1/20-1/19|+|1/19-1/18|+|1/18-1/17|+......+|1/2-1|
=1/19-1/20+1/18-1/19+1/17-1/18+……+1-½
=-1/20+1
=21/20

Answer 4

|1/20-1/19|+|1/19-1/18|+|1/18-1/17|+......+|1/2-1|
=1/19-1/20+1/18-1/19+1/17-1/18+1/16-1/17+.....+1/2-1/3+1-1/2
=-1/20+1
=19/20

Answer 5

=1/19-1/20+1/18-1/19+1/17-1/18+....1-1/2
=1-1/20
=19/20

追问

理由何在？