3) Pentru ca fractia sa fie subunitara numitorul trebuie sa fie mai mare decat numaratorul
[tex]2^{3*n}>7^{n}\\\\(2^{3})^{n}>7^{n}\\\\8^{n}>7^{n}\\\\8>7\ Adevarat\ =>\ fractia\ este\ subunitara\ pentru\ orice\ n>0[/tex]
4)
[tex][tex]\frac{2^{41}-2^{39}}{2^{40}+2^{39}}=\frac{2^{39}(2^{41-39}-2^{39-39})}{2^{39}(2^{40-39}+2^{39-39})}}\\\\\frac{2^{39}(2^{2}-2^0)}{2^{39}(2^1+2^0)}=\frac{2^{39}(4-1)}{2^{39}(2+1)}=\frac{2^{39}*3}{2^{39}*3}\ =>\\\\ Numitorul\ este\ egal\ cu\ numaratorul\ =>\ fractia\ este\ echiunitara[/tex]
