|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|...|1/10-1/9|
=(1-1/2)+(1/2-1/3)+.+(1/8-1/9)+(1/9-1/10)
=1-1/2+1/2-1/3+.+1/8-1/9+1/9-1/10
=1-1/10
=9/10