\(A=\dfrac{49}{5}-\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}\right)\)
\(A=\dfrac{49}{5}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{32}\right)\)
\(A=\dfrac{49}{5}-\left(1-\dfrac{1}{32}\right)=\text{}\dfrac{49}{5}-\dfrac{31}{32}\text{}\)
\(A=\dfrac{1413}{160}\text{}\)