Answer
$\infty$
Work Step by Step
We are given the sequence:
$\left\{\dfrac{n^{10}}{\ln^{20} n}\right\}$
Let $a_n=n^{10}$ and $b_n=\ln^{20} n$.
As $\ln^{20} n\ll n^{10}$, we have: $b_n\ll a_n$. Because $b_n$ appears before $a_n$ in the list of growth rates, using Theorem 8.6, we get:
$\lim\limits_{n \to \infty} \dfrac{a_n}{b_n}=\infty$
