Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Discrete mathematics, continuous mathematics, and probability resit / 3 / a / ii

False. Set $a_n=4^n/n^4$. For $n\ge 4$,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.