I'm trying to figure out the closed form formula for the following:

$$ \sum_{i=1}^{N} \frac{1}{i} $$

I think the denominator will have $N!$ in it but otherwise I cannot figure it out. Can someone help?


For a 'closed' form, look to this identity (but, there is no closed, closed form):


Where $\psi^{(n)}(x)$ is the nth derivative of the digamma function.

When $a=1$:


Where $\text{H}_{\text{x}}$ is the xth harmonic number and $\gamma$ is the Euler-Mascheroni constant.

| cite | improve this answer | |

Not the answer you're looking for? Browse other questions tagged or ask your own question.