How do you prove that [math]2^{\frac{1}{4}} \times 4^{\frac{1}{8}} \times 8^{\frac{1}{16}} \times \dots =2[/math]?
How can I prove that, for [math]n \geq 2[/math], [math](1+\frac{1}{n})^n < n (1+\frac{1}{n})[/math]?