Question

3²⁰¹³supra 5-2×3²⁰¹²supra 5 -2×3²⁰¹¹supra 5 -...-2×3 supra 5 Va rog ajutor!​

Answer 1

Explicație pas cu pas:

$\frac{ {3}^{2013} }{5} - \frac{2 \cdot {3}^{2012} }{5} - \frac{2 \cdot {3}^{2011} }{5} - ... - \frac{2 \cdot 3}{5} =$

$= \frac{ {3}^{2013} }{5} - \frac{2}{5} \cdot ({3}^{2012} + {3}^{2011} + ... + 3)$

$= \frac{ {3}^{2013} }{5} - \frac{2}{5} \cdot \frac{3 \cdot ( {3}^{2012} - 1)}{3 - 1}$

$= \frac{ {3}^{2013} }{5} - \frac{2}{5} \cdot \frac{{3}^{2013} - 3}{2} = \frac{ {3}^{2013} }{5} - \frac{{3}^{2013} - 3}{5}$

$= \frac{{3}^{2013} - {3}^{2013} + 3}{5} = \bf \frac{3}{5}$