1-1/2>0
1/2-1/3>0
1/3-1/4>0
.
1/9-1/10>0
∣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