4/3-7/12+9/20-11/30+13/42-15/56+17/72-19/90
=(4/3)-(1/3+1/4)+(1/4+1/5)-(1/5+1/6)+(1/6+1/7)-(1/7+1/8)+(1/8+1/9)-(1/9+1/10)
=4/3-1/3-1/4+1/4+1/5-1/5-1/6+1/6+1/7-1/7-1/8+1/8+1/9-1/9-1/10
=4/3-1/3-1/10
=9/10