Question

Eu l-am facut, doar ca vreau sa ma verific iar in carte nu exista raspunsuri

Simplificati fractia pana devine ireductibila: 2 la puterea n+ 2 la puterea n+1+ 2 la puterea n+2 supra 7 la puterea n+ 7 la puterea n+1+ 7 la puterea n+2

Answer 1

[tex]\frac{2^n+2^{n+1}+2^{n+2}}{7^n+7^{n+1}+7^{n+2}}=\frac{2^n+2^n\cdot2+2^n\cdot4}{7^n+7^n\cdot 7+7^n\cdot 49}=\frac{2^n(1+4+7)}{7^n(1+7+49)}=\frac{2^n\cdot 7}{7^n\cdot 57}=\frac{2^n}{7^{n-1}\cdot 57}\\ Nu\ mai\ am\ ce\ sa-i\ fac.[/tex]

Answer 2

(2ⁿ+2ⁿ⁺¹+2ⁿ⁺²)/(7ⁿ+7ⁿ⁺¹+7ⁿ⁺²)=2ⁿ(1+2+4)/7ⁿ(1+7+49)=2ⁿx7/7ⁿx57=2ⁿ/7ⁿ⁻¹x57