Question

Punctul b va rogggg
Dau coronita

Answer 1

   
[tex]\displaystyle\\ 34b)~\frac{3^{4n+2}-9}{8^{4n+2}+1}\\ \text{Calculam ultima cifra si la numarator si la numitor. } \\ \text{Notatie:}~U(k) = \text{ ultima cifra a lui k}\\ \frac{U(3^{4n+2}-9)}{U(8^{4n+2}+1)}=\frac{U(3^{4n+2})-U(9)}{U(8^{4n+2})+U(1)}=\frac{U(3^{4n}\cdot3^{2})-9}{U(8^{4n}\cdot8^{2})+1}=\\\\ =\frac{U(3^4)^n\cdot U(3^ {2}) -9}{U(8^4)^n\cdot U(8^{2})+1}= \frac{U(81^n)\cdot U(9) -9}{U(4096^n)\cdot U(64)+1}=\\\\ = \frac{1\cdot 9 -9}{U(6\cdot 4)+1}=\frac{0}{4+1}=\frac{0}{5} [/tex]

⇒ Se simplifica cu 5.