Asymptotics of a sinusoid Consider the function
$$
f(n) = 2n^2 |\sin(\pi \cdot n/2)|.
$$
Which of the following classes does $f(n)$ belong to?
$$ O(n^2), \Omega(n^2), \Theta(n^2), \omega(n^2), o(n^2). $$

I'm working in this and so far I have been trying to use different methods but always get to a dead end.
Let us notice the following:
$$
|\sin(\pi \cdot n/2)| = \begin{cases} 1 &amp; \text{if $n$ is odd}, \\ 0 &amp; \text{if $n$ is even}. \end{cases}
$$
This implies that your function $f(n)$ alternates between $n^2$ (for odd $n$) and $0$ (for even $n$). This means, for example, that $f(n) = O(n^2)$ (since $f(n) \leq n^2$ for all $n$) but $f(n) \neq \Omega(n^2)$ (considering even $n$).