real analysis - Evaluate $lim_{n to infty} sum_{k=n}^{2n} frac{1}{n+sqrt{k}}$

Evaluate $$\lim_{n \to \infty} \sum_{k=n}^{2n} \frac{1}{n+\sqrt{k}}$$

I tried to write the sum above as $$\lim_{n \to \infty} \frac{1}{n+\sqrt{n}} + \frac{1}{n+\sqrt{n+1}}+\dotsb+\frac{1}{n+\sqrt{2n}}$$
Now if I solve the limit the result is $0$ but obviously it's wrong. I think because it's an infinity sum of factors that go to zero, but it could be that the sum goes to infinity faster than the factors so that the result isn't zero. However I don't know how to solve it. Some advice?