Question

Answer 1

`1/2+5/6+11/12+...+89/90`

`= (1-1/2)+(1-1/6)+...+(1-1/90)`

`= (1+1+1+...1)-(1/2+1/6+...+1/90)`

`= 9-(1/(1.2)+1/(2.3)+...+1/(9.10))`

`=9-(1-1/2+1/2-1/3+...+1/9-1/10)`

`= 9-(1-1/10)`

`= 9-9/10`

`= 81/10`

Answer 2

giúp với 

Answer 3

`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)`

`=1-1/2 +1-1/6 +1-1/12 +1 - 1/20+1-1/30 +1-1/42+1-1/56+1-1/72+1-1/90`

`=1-1/2 +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)-(1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)``=9-(1/(1xx2) + 1/(2xx3) + 1/(3xx4) + 1/(4xx5) + .......+1/(9xx10)``=9 - (1-1/2+1/2-1/3+..........+1/9-1/10)``=9 -(1-1/10)``=9-(10/10-1/10)``=9-9/10``=90/10-9/10``=81/10`