Răspuns:
0
Explicație pas cu pas:
[tex]n - > inf[/tex]
[tex]lim \frac{ {2}^{n} + {3}^{n} }{ {3}^{n} + {4}^{n} } = lim \frac{ \frac{{2}^{n}}{{4}^{n}} + \frac{{3}^{n}}{{4}^{n}}}{\frac{{3}^{n}}{{4}^{n}} +\frac{{4}^{n}}{{4}^{n}} } \\ = lim \frac{( \frac{1}{2} )^{n} + ( \frac{3}{4})^{n} }{ (\frac{3}{4} )^{n} + 1} \\ = \frac{lim(( \frac{1}{2} )^{n} + ( \frac{3}{4})^{n} )}{lim((\frac{3}{4} )^{n} + 1)} \\ = \frac{0}{1} = 0[/tex]
