Răspuns
1
Explicație pas cu pas:
[tex]\displaystyle \limit\lim_{n\to\infty}\dfrac{n}{\ln n}\cdot \left(\sqrt[n]{n}-1\right)= \lim_{n\to\infty}\dfrac{n}{\ln n} \left(e^{\frac{\ln n}{n}}-1 \right)= \lim_{n\to\infty} \dfrac{e^{\frac{\ln n}{n}}-1}{\frac{\ln n}{n}} =\\= \ln e =\boxed{1}[/tex]
