Hi. I have a feeling this is kinda a known thing, but I don't know it, so hopefully you can help me out. I'm a lowly software developer.

For a given n and k, is there a short-cut way of calculating (or approximating) the value of this expression?

$\sum_{n}^{k}\frac{1}{n}$

It's a matter of computational efficiency: I have a lot of these expressions i want to calculate.