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What is the rate of growth of the partial sums of the reciprocals of the odd numbers?

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    This was in fact shown and used recently here: http://math.stackexchange.com/questions/13888/how-to-sum-frac11-cdot-2-cdot-3-cdot-4-frac43-cdot-4-cdot-5-cdot-6-fr/13894#138942010-12-13
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    Thank you for helpful comment.2010-12-13

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$\sum_{1}^{n} \frac{1}{2i-1} = \sum_{1}^{2n} \frac{1}{i} - \frac{1}{2}\sum_{1}^{n} \frac{1}{i}$, and this is approximately $\ln(2n) - \frac{1}{2}\ln(n)+\frac{1}{2} \gamma = \frac{1}{2} \ln(n) + \ln(2) + \frac{1}{2} \gamma$ for large $n$.

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    Thank you, Barry! $\gamma$ means Euler–Mascheroni constant?2010-12-13
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    Yes, it does indeed.2010-12-13