find the interval and radius of convergence for sum from n=1 to infinity of $\displaystyle \frac{x^n}{\sqrt{n}}$. So I used the ratio test and I've got it down to $\displaystyle |x| \lim_{n\to\infty}|\sqrt{\frac{n}{n+1}}|$. I want to use L'Hospitals rule but I'm uncertain how to proceed. Can I use L'H rule on $\displaystyle \frac{n}{n+1}$ or do I use it on $\displaystyle \frac{\sqrt{\frac{n}{n+1}}}{1}$