$\lim_{n \to \infty} \frac{a_n}{b_n} = 0$

$\lim_{n \to \infty} \frac{a_n}{b_n} = L$ where $0 < L < \infty$

$\lim_{n \to \infty} \frac{a_n}{b_n} = \infty$

All limits lead to the same conclusion about convergence