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I know this statement is true... but how do I prove it?

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 Alas, but this is not the right place to ask this question. Please try math.stackexchange.com instead. – Deane Yang Oct 5 2011 at 4:20
For any $y>0$ we have $\ln(1+y)=\int_0^y \frac{dt}{1+t} < \int_0^y 1 = y$. Now write $y=1/x$ on the two sides, done. BTW this question is not appropriate on this site, read the FAQ. Voting to close. – GH Oct 5 2011 at 4:22

closed as too localized by Qiaochu Yuan, Deane Yang, GH, Ricky Demer, Gjergji Zaimi Oct 5 2011 at 4:26

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