1/2 + 5/6 + 11/12 + 19/20+ 29/30 +41/42+55/56+71/72+89/90
= 1 -1/2 +1-1/6+1- 1/12+1-1/20 + 1-1/30+1-1/42+ 1-1/56+1-1/72+1-1/90
=(1+1+1+1+1+1+1+1+1)-(1/1-1/2+1/2-1/3+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)
=9-(1 -1/10)
=9-9/10
=81/10