How can I prove [math]\displaystyle \lim_{n\to\infty}\sqrt[n]{n^k}=1[/math], where [math]k \in N^+[/math]?
How can I prove that, for [math]n \geq 2[/math], [math](1+\frac{1}{n})^n < n (1+\frac{1}{n})[/math]?