\(A=1-\dfrac{1}{6}+1-\dfrac{1}{12}+...+1-\dfrac{1}{132}\)
\(=9-\left(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{132}\right)\)
\(=9-\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{11}-\dfrac{1}{12}\right)\)
\(=9-\left(\dfrac{1}{2}-\dfrac{1}{12}\right)=9-\dfrac{5}{12}=\dfrac{103}{12}\)