Đáp án:
Giải thích các bước giải:
Đặt $A=3-{{3}^{2}}+...+{{3}^{19}}-{{3}^{20}}$
$\to 3A={{3}^{2}}-{{3}^{3}}+...+{{3}^{20}}-{{3}^{21}}$
$3A+A=\left( {{3}^{2}}-{{3}^{3}}+...+{{3}^{20}}-{{3}^{21}} \right)+\left( 3-{{3}^{2}}+...+{{3}^{19}}-{{3}^{20}} \right)$
$4A=\left( {{3}^{2}}-{{3}^{2}} \right)+\left( {{3}^{3}}-{{3}^{3}} \right)+...\left( {{3}^{20}}-{{3}^{20}} \right)+3-{{3}^{21}}$
$4A=3-{{3}^{21}}$
$A=\frac{3-{{3}^{21}}}{4}$
