# The rate of growth of the partial sums of the reciprocals of the odd numbers

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

$\sum_{1}^{n} \frac{1}{2i-1} = \sum_{1}^{2n} \frac{1}{i} - \frac{1}{2}\sum_{1}^{n} \frac{1}{i}$, 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 $n$.
• Thank you, Barry! $\gamma$ means Euler–Mascheroni constant? – Oleksandr Bondarenko Dec 13 '10 at 19:58