|1/2-1|+|1/3-1/2|+|1/4-1/3|+…+|1/10-1/9|
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/9-1/10)
=1-1/2+1/2-1/3+1/3-1/4+...+1/9-1/10
=1-1/10
=9/10
|1/2-1|+|1/3-1/2|+|1/4-1/3|+…+|1/10-1/9|
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/9-1/10)
=1-1/2+1/2-1/3+1/3-1/4+...+1/9-1/10
=1-1/10
=9/10