Đáp án:
$\begin{array}{l}
a)A = 1 + \dfrac{1}{2} + {\left( {\dfrac{1}{2}} \right)^2} + {\left( {\dfrac{1}{2}} \right)^3} + {\left( {\dfrac{1}{2}} \right)^4} + {\left( {\dfrac{1}{2}} \right)^5}\\
\Rightarrow 2.A = 2 + 1 + {\left( {\dfrac{1}{2}} \right)^2} + {\left( {\dfrac{1}{2}} \right)^3} + {\left( {\dfrac{1}{2}} \right)^4}\\
b)2A - A\\
= \left( {2 + 1 + {{\left( {\dfrac{1}{2}} \right)}^2} + {{\left( {\dfrac{1}{2}} \right)}^3} + {{\left( {\dfrac{1}{2}} \right)}^4}} \right)\\
- \left( {1 + \dfrac{1}{2} + {{\left( {\dfrac{1}{2}} \right)}^2} + {{\left( {\dfrac{1}{2}} \right)}^3} + {{\left( {\dfrac{1}{2}} \right)}^4} + \left( {\dfrac{1}{2}} \right)} \right)\\
\Rightarrow A = 2 - {\left( {\dfrac{1}{2}} \right)^5}\\
= - {\left( {\dfrac{1}{2}} \right)^5} + 2
\end{array}$
