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My question is:

Prove or disprove: For any number $n\in \mathbb{Z}$ and $n > 0$, $$n \ge H_n = \sum_{k=1}^n \frac{1}{k}.$$

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Note that $$h(n) = \sum_{i = 1}^n \frac{1}{i}$$ and $$n = \sum_{i=1}^n 1.$$ Now hopefully you can see how to compare these two quantities to confirm your suspicion.

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  • $\begingroup$ Dang! It's been a while since I have done math, and I just threw it up there. Thank you! $\endgroup$
    – Don Code
    Dec 3, 2013 at 8:39

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