Example of Little-oh

Question

The question is: A simple example of a function that is $o(n)$ is $\ln(n)$. Give another example of a non-negative, non-constant function that is $o(n)$.

I thought about using $f(n) = 10n - n\ln(n)$ but I am not sure if it's a good enough answer since, for extremely large values of n, $lim_{n→∞}\frac{f(n)}{g(n)} < 0$

Any suggestions?

Answer 1

You could use any $|n|^z$ where $z<0$. Or you could use $e^{-\sqrt{n}}$; there are many functions that could work.