[tex] \displaystyle \frac{3^{2013}}{5} - \frac{2\cdot 3^{2012}}{5} -...- \frac{2\cdot 3}{5} =\\
= \frac{1}{5} [3^{2013}-2(3^{2012}+3^{2011}+...+3^1)]=\\
= \frac{1}{5} (3^{2013}-2\cdot3 \cdot \frac{3^{2012}-1}{3-1} )=\\
= \frac{1}{5} \cdot(3^{2013}-3^{2013}+3)= \frac{3}{5} [/tex]
