## Ratio test for $\frac{\sqrt{n^n}}{2^n}$ February 11 2

Before I tried root test, I did ratio test for $\frac{\sqrt{n^n}}{2^n}$ and got: $$\lim_{n\to\infty}\frac{\sqrt{(n+1)^{(n+1)}}}{2^{n+1}}\cdot \frac{2^n}{\sqrt{n^n}} = \lim_{n\to\infty} \frac{1}{2}\cdot \sqrt{\frac{(n+1)^{(n+1)}}{n^n}} = \frac{1}{2}$$