Đáp án :
`A=(3^(101)-3)/2`
`B=(3^(2012)-1)/4`
Giải thích các bước giải :
`A=3+3^2+3^3+...+3^(100)`
`<=>3A=3^2+3^3+3^4+...+3^(101)`
`<=>3A-A=3^2+3^3+3^4+...+3^(101)-3-3^2-3^3-...-3^(100)`
`<=>2A=3^(101)-3`
`<=>A=(3^(101)-3)/2`
Vậy `A=(3^(101)-3)/2`
`B=3^(2011)-3^(2010)+...+3^3-3^2+3-1`
`<=>3B=3^(2012)-3^(2011)+...+3^4-3^3+3^2-3`
`<=>3B+B=3^(2012)-3^(2011)+...+3^4-3^3+3^2-3+3^(2011)-3^(2010)+...+3^3-3^2+3-1`
`<=>4B=3^(2012)-1`
`<=>B=(3^(2012)-1)/4`
Vậy `B=(3^(2012)-1)/4`
