|1/10-1/9|+|1/9-1/8|+|1/8-1/7|...+|1/2-1|
= 1/9 - 1/10 + 1/8 - 1/9 + 1/7 - 1/8 + ...+ 1 - 1/2
= 1 - 1/10
= 9/10