\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+\frac{1}{3^5}+\frac{1}{3^6}\)
\(3A=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+\frac{1}{3^5}\)
=> \(2A=1-\frac{1}{3^6}\)
=> \(A=\frac{1-\frac{1}{3^6}}{2}=\frac{729-1}{729}.\frac{1}{2}=\frac{728}{729.2}=\frac{364}{729}\)