Đáp án:
A>B
Giải thích các bước giải:
\(\begin{array}{l}
\dfrac{3}{2}A = \dfrac{3}{2}.\dfrac{1}{2} + {\left( {\dfrac{3}{2}} \right)^2} + {\left( {\dfrac{3}{2}} \right)^3} + .... + {\left( {\dfrac{3}{2}} \right)^{2012}} + {\left( {\dfrac{3}{2}} \right)^{2013}}\\
\Rightarrow \dfrac{3}{2}A - A = {\left( {\dfrac{3}{2}} \right)^{2013}} + \dfrac{3}{4} - \dfrac{3}{2} - \dfrac{1}{2}\\
\dfrac{A}{2} = {\left( {\dfrac{3}{2}} \right)^{2013}} - \dfrac{5}{4}\\
\Rightarrow A = 2.{\left( {\dfrac{3}{2}} \right)^{2013}} - \dfrac{5}{2} > {\left( {\dfrac{3}{2}} \right)^{2013}}:2\\
\Rightarrow A > B
\end{array}\)
