If I evaluate a limit as n goes to infinity and I have a O(1/n^3) term being multiplied by n^3, then does this term still go to zero in the limit?

Question

The term would then be in O(1), I believe. Do I still interpret this term as having a limit of zero, as n goes to infinity?

Thanks,

Answer 1

Not necessarily. By definition $O(1)$ is a map $f$ such that there is some $M \geq 0$ such that $|f(x)| \leq M$ for all suitable $x$.