Evaluating $\lim_{n \to \infty} \sum_{k=1}^n \frac{1}{ n + k}$

Question

I'm having some trouble evaluating the following limit:

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

I think that I'm supposed to transform this into an integral using Riemann Sums. How should I proceed? Because I can't see anything that resembles a Riemann sum.

Answer 1

Using Stadnicki comment, it looks like the limit is$\int_0^1\frac{1}{1+x}dx=ln(2)$.