Is there a closed form expression for the sum of the reciprocal values of the first n natural numbers?

Question

Does there exist a closed form expression for this sum?

$$ \sum\limits_{i=1}^n \frac {1}{i} $$

Answer 1

You would have to define what "closed" means. As far as I can tell, $\displaystyle \sum_{i=1}^n\frac1i$ is a closed as it can get.