Đáp án:
$\begin{array}{l}
A = {2010^3} + \left( {{{2010}^1} + {{2010}^2} + ... + {{2010}^{20}}} \right)\\
Đặt:B = {2010^1} + {2010^2} + ... + {2010^{20}}\\
\Rightarrow 2010.B = {2010^2} + {2010^3} + ... + {2010^{21}}\\
\Rightarrow 2010.B - B = {2010^{21}} - 2010\\
\Rightarrow B = \dfrac{{{{2010}^{21}} - 2010}}{{2009}}\\
\Rightarrow A = {2010^3} + \dfrac{{{{2010}^{21}} - 2010}}{{2009}}\\
= \dfrac{{{{2010}^3}.2009 + {{2010}^{21}} - 2010}}{{2009}}
\end{array}$
