Explicație pas cu pas:
[tex]\frac{ {3}^{2013} }{5} - \frac{2 \cdot {3}^{2012} }{5} - \frac{2 \cdot {3}^{2011} }{5} - ... - \frac{2 \cdot 3}{5} = \\ [/tex]
[tex]= \frac{ {3}^{2013} }{5} - \frac{2}{5} \cdot ({3}^{2012} + {3}^{2011} + ... + 3) \\ [/tex]
[tex]= \frac{ {3}^{2013} }{5} - \frac{2}{5} \cdot \frac{3 \cdot ( {3}^{2012} - 1)}{3 - 1} \\ [/tex]
[tex]= \frac{ {3}^{2013} }{5} - \frac{2}{5} \cdot \frac{{3}^{2013} - 3}{2} = \frac{ {3}^{2013} }{5} - \frac{{3}^{2013} - 3}{5} \\ [/tex]
[tex]= \frac{{3}^{2013} - {3}^{2013} + 3}{5} = \bf \frac{3}{5} \\ [/tex]
