What is the rate of growth of the partial sums of the reciprocals of the odd numbers?
The rate of growth of the partial sums of the reciprocals of the odd numbers
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sequences-and-series
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0Thank you for helpful comment. – 2010-12-13
1 Answers
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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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0Yes, it does indeed. – 2010-12-13