Question

Habar nu am :(..... ​

Answer 1

$\displaystyle{ 2^{n+1} \cdot 3^{n} + 5 \cdot 6^{n} = 2^{n} \cdot 2 \cdot 3^{n} + 5 \cdot 6^{n} }$

$\displaystyle{ = 2^{n} \cdot 3^{n} \cdot 2 + 6^{n} \cdot 5 }$

$\displaystyle{ =6^{n} \cdot 2 + 6^{n} \cdot 5 }$

$\displaystyle{ = 6^{n} \cdot (2 + 5) }$

$\displaystyle{ = 6^{n} \cdot 7 }$

ceea ce evident se divide cu7

q.e.d.