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How do you simplify \[\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}\] or maybe a generalisation, like \[\sum_{n=1}^{x}\frac{1}{n}?\] I don't know any way to do this so far. I've tried to split it into partial fractions, but was not able to do it. Any form of simplification would be fine.

Note by Victor Loh
2 years, 9 months ago

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As x approaches infinity, the sum approaches infinity. Daniel Leong · 2 years, 8 months ago

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There is no closed formula for your sum. You can find more information here: http://en.wikipedia.org/wiki/Harmonic_number Jon Haussmann · 2 years, 9 months ago

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Is not possible to obtain a closed formula using elementary functions, maybe this link will help you: link Jorge Tipe · 2 years, 9 months ago

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