Past exam of the year 1 of the computer science course of the University of Oxford / 2022 / Discrete mathematics, continuous mathematics and probability resit / 2 / c / iii

True. Rationalization gives, for $n\ge 1$,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.