I don't know how Debian planet deals with MathJax (it seems to become illegible), but I will try to post this, anyway.


Fact: Since the harmonic numbers can be approximated by the natural logarithm, that is, \(H_n \simeq \ln n\), we can clearly see that \[ \frac{1}{i+1} + \cdots + \frac{1}{n} = H_n - H_i \simeq \ln n - \ln i = \ln \frac{n}{i}, \] which is a trivial approximation that may be handy sometimes.

If you spot any errors on this, please let me know.

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