Hi, I need an upper bound for the generalized harmonic number with negative exponents, i.e:

$$H_{n,r}=\sum_{k=1}^n \frac{1}{k^r}$$

where $r<0$ especially, I need a bound for $$r=-\frac{1}{2}$$ Has anyone an idea whether those bounds exist? Thanks!

PS: I've seen the related question, but the answer only deals with $$r>0$$