Question

Exercitiul 6

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Answer 1

[tex]6. \frac{5^{n+1}-5^n+2\cdot5^{n+2}}{2^{n+5}-2^{n+2}-2^n}=\\ \frac{5^n\cdot 5 -5^n +2\cdot5^n\cdot 5^2}{2^n\cdot 2^5-2^n\cdot 2^2-2^n}=\\ \frac{5^n(5-1+2\cdot 5^2)}{2^n(2^5-2^2-1)}=\\ \frac{5^n\cdot 54}{2^n\cdot 27}=\frac{5^n}{2^{n-1}}[/tex]