$\sum_{k=1}^nH_k = (n+1)H_n-n$. Why?
This is motivated by my answer to this question.
The Wikipedia entry on harmonic numbers gives the following identity:
$$ \sum_{k=1}^nH_k=(n+1)H_n-n $$
Why is this?
Note that I don't just want a proof of this fact (It's very easily done by
induction, for example). Instead, I want to know if anyone's got a really
nice interpretation of this result: a very simple way to show not just
that this relation is true, but why it is true.
Has anyone got a way of showing that this identity is not just true, but
obvious?
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