\(S=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{2017}}\)
\(3S=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{2016}}\)
\(3S-S=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{2016}}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{2017}}\right)\)
\(2S=1-\frac{1}{3^{2017}}\)
\(\Rightarrow S=\frac{1-\frac{1}{3^{2017}}}{2}\)