Đáp án :
`A=(3^(2010)+1)/2`
Giải thích các bước giải :
`A=3^(2010)-(3^(2009)+3^(2008)+3^(2007)+...+3^2+3+1)`
`+)Đặt B=3^(2009)+3^(2008)+3^(2007)+...+3^2+3+1`
`<=>3B=3^(2010)+3^(2009)+3^(2008)+...+3^3+3^2+3`
`<=>3B-B=(3^(2010)+3^(2009)+...+3^2+3)-(3^(2009)+3^(2008)+...+3+1)`
`<=>2B=3^(2010)-1`
`<=>B=(3^(2010)-1)/2`
`<=>A=3^(2010)-(3^(2010)-1)/2`
`<=>A=[2.3^(2010)]/2-(3^(2010)-1)/2`
`<=>A=(2.3^(2010)-3^(2010)+1)/2`
`<=>A=(3^(2010)+1)/2`
Vậy `A=(3^(2010)+1)/2`
~Chúc bạn hoc tốt !!!~
