For what $p$ values does the series $\sum_{n=1}^\infty \sqrt{n^{p-4}}$ converge? For what $p$ values does the series $\sum_{n=1}^\infty \sqrt{n^{p-4}}$ converge?
I think it's $\forall p\in[1,2)$, but I can't show it.

Let $p \in \mathbb{R}$. Then $\sum_{n} n^{\frac{p-4}{2}}$ converges if and only if $\frac{p-4}{2} < -1$, that is, $p < 2$.
