Definition:Asymptotic Equality/Sequences/Definition 1

Definition
Let $\sequence {a_n}$ and $\sequence {b_n}$ be sequences in $\R$. Let $b_n \ne 0$ for all $n$.

$\sequence {a_n}$ is asymptotically equal to $\sequence {b_n}$ :
 * $\ds \lim_{n \mathop \to \infty} \dfrac {a_n} {b_n} = 1$

Also see

 * Equivalence of Definitions of Asymptotically Equal Sequences