C

Gọi\(A=\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^8}\)

\(\Rightarrow3A=1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^7}\)

\(\Rightarrow2A=\left(1+\dfrac{1}{3}+...+\dfrac{1}{3^7}\right)-\left(\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^8}\right)\)

\(\Rightarrow2A=1-\dfrac{1}{3^8}\)

\(\Rightarrow A=\dfrac{1}{2}-\dfrac{1}{3^8.2}\)