Tính `1/2` + `5/6` + `11/12` +... + `89/90` + `109/110` - `10/11`

Đáp án:

`=90/11`

Giải thích các bước giải:

`1/2 + 5/6 +11/12 + ... + 89/90 + 109/110 - 10/11`

`= ( 1 - 1/2 ) + ( 1- 1/6) +...+(1-1/90) + (1-1/110) - 10/11`

`= ( 1+1+1+..+1) - ( 1/2 + 1/6 + ...+1/110) - 10/11`

`= 10 xx 1 - ( 1/(1*2) +1 /(2*3) + ...+ 1/(10*11))-1/10/11`

`= 10 - ( 1-1/2+1/2-1/3+...+ 1/10 - 1/11)-10/11`

`= 10 - ( 1 - 1/11) - 10/11`

`=10 - 10/11-10/11`

`= 10 - (10/11+10/11)`

`= 10 - 20/11`

`= 110/11 - 20/11`

`= 90/11`

`~nhungan~`