tính nhanh : 3/2 + 7/6 + 13/12 + 21/20 + ...... + 91/90 + 111/110

Đáp án:

`3/2+7/6+13/12+21/20+...+91/90+111/110`

`=(1+1/2)+(1+1/6)+(1+1/12)+(1+1/20)+...+(1+1/90)+(1+1/110)`

`\underbrace{(1+1+1+1+...+1+1)}_{\text{10 số}}+(1/2+1/6+1/12+1/20+..+1/90+1/110)`

`=10+(1/(1xx2)+1/(2xx3)+1/(3xx4)+1/(4xx5)+...+1/(9xx10)+1/(10xx11))`

`=10+(1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/9-1/10+1/10-1/11)`

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

`=10+10/11`

`=120/11`