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Is there an elementary proof that $\sum \limits_{k=1}^n \frac1k$ is never an integer?

Let $n>1$, then prove that $\;1+\dfrac{1}{2}+\dfrac{1}{3}+\cdots +\dfrac{1}{n}\;$ is not an integer.



marked as duplicate by draks ..., Namaste, leonbloy, Clive Newstead, sdcvvc Nov 27 '12 at 14:45

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