\(1)C=\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+...+\dfrac{1}{162}\)
\(3C=1+\dfrac{1}{3}+\dfrac{1}{9}+...+\dfrac{1}{54}\)
\(3C-C=\left(1+\dfrac{1}{3}+\dfrac{1}{9}+...+\dfrac{1}{54}\right)-\left(\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+...+\dfrac{1}{162}\right)\)
\(2C=1-\dfrac{1}{162}\)
\(2C=\dfrac{161}{162}\)
\(C=\dfrac{161}{162}.\dfrac{1}{2}\)
\(C=\dfrac{161}{324}\)
\(2)A=\dfrac{1}{2}+\dfrac{1}{8}+\dfrac{1}{32}+\dfrac{1}{128}+\dfrac{1}{512}\)
\(2A=1+\dfrac{1}{2}+\dfrac{1}{8}+\dfrac{1}{32}+\dfrac{1}{128}\)
\(2A-A=\left(1+\dfrac{1}{2}+\dfrac{1}{8}+\dfrac{1}{32}+\dfrac{1}{128}\right)-\left(\dfrac{1}{2}+\dfrac{1}{8}+\dfrac{1}{32}+\dfrac{1}{128}+\dfrac{1}{512}\right)\)
\(A=1-\dfrac{1}{512}=\dfrac{511}{512}\)
