Question

fracţia 5 ori 4 la puterea n ori 3 la puterea n +1 plus 4 la puterea n +1 ori 3 la puterea n +2 supra 12 la puterea n+1 + 5 ori 12 la puterea n
este egală cu un număr natural;​

Answer 1

Răspuns: 3

Explicație pas cu pas:

Salutare!

$\mathbf{\dfrac{5\cdot 4^{n}\cdot 3^{n+1}+4^{n+1}\cdot3^{n+2}}{12^{n+1}+5\cdot12^{n}}}=$

$\mathbf{\dfrac{4^{n}\cdot 3^{n+1}\cdot\bigg(5\cdot 4^{n-n}\cdot 3^{n+1-(n-1)}\bigg)+4^{n}\cdot 3^{n+1}\cdot\bigg(4^{n+1-n}\cdot3^{n+2-(n+1)}\bigg)}{12^{n}\cdot\bigg(12^{n+1-n}+5\cdot12^{n-n}\bigg)}}=$

$\mathbf{\dfrac{4^{n}\cdot 3^{n+1}\cdot\bigg(5\cdot 4^{0}\cdot 3^{0}\bigg)+4^{n}\cdot 3^{n+1}\cdot\bigg(4^{1}\cdot3^{1}\bigg)}{12^{n}\cdot\bigg(12^{1}+5\cdot12^{0}\bigg)}}=$

$\mathbf{\dfrac{4^{n}\cdot 3^{n+1}\cdot\bigg(5\cdot1\cdot 1\bigg)+4^{n}\cdot 3^{n+1}\cdot\bigg(4\cdot 3\bigg)}{12^{n}\cdot\bigg(12+5\cdot1\bigg)}}=$

$\mathbf{\dfrac{4^{n}\cdot 3^{n+1}\cdot\bigg(5\cdot1+12\bigg)}{12^{n}\cdot\bigg(12+5\bigg)}=\dfrac{4^{n}\cdot 3^{n}\cdot 3 \cdot 17}{12^{n}\cdot 17}=\dfrac{\not4^{n}\cdot\not 3^{n}\cdot 3 \cdot\not 17}{\not 12^{n}\cdot \not 17}=\boxed{\boxed{\bf 3}}}$

#copaceibrainly