What is [math]\displaystyle \lim_{n \to \infty}\scriptstyle \sqrt{1+ \sqrt{2 +\sqrt{3 + \sqrt{\ldots \sqrt{n}}}}}[/math]? What is [math]\displaystyle \lim_{n \to \infty}\scriptstyle \sqrt{1 +2 \sqrt{1 +3 \sqrt{1 +4 \sqrt{\ldots \sqrt{1+n}}}}}[/math]?