\textbf{113-} For natural numbers $n \geq n_0$, the sequence $\left\{\dfrac{2n^2+1}{n^2+2n}\right\}$ converges to its limit point, with a distance less than $0.04$. The smallest value of $n_0$ is which of the following?
\medskip
(1) $96$ \hfill (2) $97$ \hfill (3) $98$ \hfill (4) $99$
\bigskip