Is $\lim_{n \rightarrow \infty} a_{n+1}/a_n=L \implies \lim_{n \rightarrow \infty} \sqrt [n] {a_n}=L$ true? If not, is there a counter example?
Limit of ${a_n}^{1/n}$ is equal to $\lim_{n\to\infty} a_{n+1}/a_n$