Question

va rog am nevoie pana luni ​

Answer 1

Explicație pas cu pas:

$\dfrac{ {2}^{n + 1} \cdot {3}^{n} + {2}^{n} \cdot {3}^{n + 1} + {6}^{n}}{{2}^{n + 1} \cdot {3}^{n + 1} + 5 \cdot {6}^{n}} = \dfrac{2 \cdot {(2 \cdot 3)}^{n} + 3 \cdot {(2 \cdot 3)}^{n} + {6}^{n}}{{(2 \cdot 3)}^{n + 1} + 5 \cdot {6}^{n}} =$

$= \dfrac{2 \cdot {6}^{n} + 3 \cdot {6}^{n} + {6}^{n}}{{6}^{n + 1} + 5 \cdot {6}^{n}} = \dfrac{{6}^{n} \cdot (2 + 3 + 1)}{{6}^{n + 1} + 5 \cdot {6}^{n}}$

$= \dfrac{{6}^{n} \cdot 6}{{6}^{n + 1} + 5 \cdot {6}^{n}} = \dfrac{{6}^{n + 1}}{{6}^{n + 1} + 5 \cdot {6}^{n}} < 1$