Solution
= Solution
\b[True.] Rationalization gives, for $n\geq1$,
$$
\sqrt{4n^2+n}-2n
=\frac n{\sqrt{4n^2+n}+2n}
=\frac1{\sqrt{4+1/n}+2}.
$$
This lies between zero and $1/4$, so it is $O(1)$ in <Big O notation>. In fact it converges to $1/4$, rather than to zero. The rationalized form also avoids the <catastrophic cancellation> of subtracting two nearby large quantities.