\liminf_{n \to \infty}{\frac{a_{n+1}}{a_n}}\leq\liminf_{n \to \infty}{\sqrt[n]{a_n}}\leq\limsup_{n \to \infty}{\sqrt[n]{a_n}}\leq\limsup_{n \to \infty}{\frac{a_{n+1}}{a_n}}