Definition:Little-O Notation/Sequence/Definition 2

Definition
Let $\sequence {a_n}$ and $\sequence {b_n}$ be sequences of real or complex numbers.

Let $b_n \ne 0$ for all $n$.

$a_n$ is little-$\oo$ of $b_n$ :
 * $\ds \lim_{n \mathop \to \infty} \frac {a_n} {b_n} = 0$

Also see

 * Equivalence of Definitions of Little-O Notation for Sequences