Solution
= Solution
\b[False.] Set $a_n=4^n/n^4$. For $n\geq4$,
$$
\frac{a_{n+1}}{a_n}=4\left(\frac n{n+1}\right)^4\geq4\left(\frac45\right)^4=\frac{1024}{625}>1.
$$
Iteration gives a growing <geometric sequence> as a lower bound for $a_n$. Hence $a_n\to\infty$ and no eventual constant can bound $4^n/n^4$, as <Big O notation> would require.