Rozwiązanie:
[tex]c)[/tex]
[tex]$ \lim_{n \to \infty} \sqrt[n]{7^{n}+5^{n}+2^{n}} = \lim_{n \to \infty} \sqrt[n]{7^{n}\Big(1+ \frac{5^{n}}{7^{n}} +\frac{2^{n}}{7^{n}} \Big)} \iff \lim_{n \to \infty} \sqrt[n]{7^{n}} =7[/tex]
[tex]d)\\[/tex]
[tex]$ \lim_{n \to \infty} \Big(1+\frac{1}{3n} \Big)^{n+2}=\lim_{n \to \infty} \Big[\Big(1+\frac{1}{3n} \Big)^{3n }\Big]^{\frac{n+2}{3n} }= \lim_{n \to \infty} e^{\frac{n+2}{3n} }=\sqrt[3]{e}[/tex]
