This is along the lines of Problem 9.8. in 'Concrete Mathematics' by Graham, Knuth and Patashnik.
Does any of the relation $\prec$, $\succ$ or $\sim$ exist between functions $f(n) =\displaystyle \sum_{k=0}^{n}k^{\lfloor \cos (k) \rfloor}$ and $g(n) =n^{\frac{3}{2}}$?
Both definitely diverge monotone to infinity, but I can't get my head around the rest.