Does $\lim_{n \to \infty} |a_n|^{\frac{1}{n}}=l$ imply $\lim_{n \to \infty} \frac{|a_{n+1}|}{|a_n|}=l$?
Are the limits $\lim\limits_{n\to \infty }\left|\frac{a_{n+1}}{a_n}\right|\,$ and $\lim\limits_{n\to \infty }\sqrt[n]{|a_n|}\,$ equal?