$\lim n(1 - \frac{a_{n+1}}{a_n}) > 1$

$\lim n(1 - \frac{a_{n+1}}{a_n}) < 1$

$\lim n(1 - \frac{a_{n+1}}{a_n}) = 0$

$\lim \frac{a_{n+1}}{a_n} = 1$