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Here is a problem concerning (hopefully!) Harmonic numbers:

Suppose that someone 'partitions' a natural number $n>0$ into $j$ 'parts' $m_k$, such that $\sum\limits_{k=1}^j m_k=n$. Since harmonic numbers series diverge, I conclude that also $\sum_{k=1}^j \frac{1}{m_k}$ diverges. The question is "is there a way to relate the last sum with the harmonic numbers?"

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    Did you intend the upper bound of the summation to be $n$ instead of $j$? I don't understand what it means for a finite sum to diverge.2011-05-04
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    I think he wanted the second summation to go from $1$ to $j$, but did you want to take the limit of the summation as $j \rightarrow \infty$?2011-05-04
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    @Qiaochy, @Nicolas: yes the second summation is from 1 to j. Yes I would like to see the behavior as n tends to infinity2011-05-04

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