Is $ \ {|{n^2\cdot \cos{(n\pi})|}\over {3n^2-5n^3 }} = \ {n^2\over 3n^2-5n^3} $ right?

Question

Is $ \ {|{n^2 \cdot \cos (n\pi)|}\over {3n^2-5n^3 }} = \ {n^2\over 3n^2-5n^3} $ correct? If yes, why?

Answer 1

Yes, it is correct. The reason is that $\cos(n\pi)$, where $n$ is an integer, is either $+1$ or $-1$. Thus $|\cos(\pi n)|=1$.

In total, $$|n^2\cos(n\pi)| = |n^2||\cos(n\pi)| = |n^2| = n^2.$$