Cho A=$\frac{1}{1.21}$+$\frac{1}{2.22}$+$\frac{1}{23.23}$+...+$\frac{1}{80.100}$;B=$\frac{1}{1.81}$+$\frac{1}{2.82}$+$\frac{1}{3.83}$+...+$\frac{1}{20.100}$.Tính$\frac{A}{B}$ Help con với các sư phụ ơi!

Đáp án:

 `A/B=4`.  

Giải thích các bước giải:

Sửa đê `:`

 `A=1/1.21+1/2.22+1/3.23+...1/80.100`

`=>20A=20/1.21+20/2.22+20/3.23+...+20/80.100`

`=1-1/21+1/2-1/22+1/3-1/23+...+1/80-1/100`

`=(1+1/2+1/3+...+1/80)-(1/21+1/22+1/23+1/100)`

`B=1/1.81+1/2.82+1/3.83+....+1/20.100`

`=>80B=80/1.81+80/2.82+80/3.83+....+80/20.100`

`=1-1/81+1/2-1/82+1/3-1/83+....+1/20-1/100`

`=(1+1/2+1/3+...+1/20)-(1/81+1/82+1/83+...+1/100)`

`=(1+1/2+1/3+...+1/20)+(1/21+1/22+...+1/80)-(1/21+1/22+...+1/80)-(1/81+1/82+1/83+...+1/100)`

`=(1+1/2+1/3+....+1/20+1/21+...+1/80)-(1/21+1/22+...+1/80+1/81+....+1/100)`

`=(1+1/2+1/3+...+1/80)-(1/21+1/22+...+1/100)`

`=20A`

`=>80B=20A` 

`=>4B=A=>A/B=(4B)/B=4`

Vậy, `A/B=4`. 

`@nguyen``nam500#hoidap247`.