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3 la puterea 2013 supra 5 mius 2 ori 3 la puterea 2012 supra 5 minus 2 ori 3 la puterea 2011 minus ... minus 2 ori 3 supra 5

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[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]

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