`B=1/3+2/9+3/27+....+2019/3^2019`

`=>B=1/3+2/3^2+3/3^3+....+2019/3^2019`

`=>3B=1+2/3+3/3^2+....+2019/3^2018`

`=>3B-B=(1+2/3+3/3^2+....+2019/3^2018)-(1/3+2/3^2+3/3^3+....+2019/3^2019)`

`=>2B=1+1/3+1/3^2+....+1/3^2018-2019/3^2019`

`=>2B<1+1/3+1/3^2+....+1/3^2018``(1)`

Đặt `A=1+1/3+1/3^2+....+1/3^2018`

`=>3A=3+1+1/3+....+1/3^2017`

`=>3A-A=(3+1+1/3+....+1/3^2017)-(1+1/3+1/3^2+....+1/3^2018)`

`=>2A=3-1/3^2018`

`=>A=3/2-1/3^2018.2`

`=>A<3/2(2)`

Từ `(1)` và `(2)` `=>2B<3/2`

`=>B<3/4`