How can I get a good estimation of the following function The function is 
$$ f(n) = \sum_{i=1}^{n} \frac{1}{2i-1}$$
How can I compute for example $f(20)$ or $f(50)$ without using a calculator. I want to have an approximation

It's a harmonic sum with odd terms: 
$$
S_n = 1 + \frac{1}{3} + \ldots \frac{1}{2n-1} = 1 +\frac{1}{2}+\frac{1}{3}  + \ldots \frac{1}{2n} - \frac{1}{2}-\frac{1}{4} -\ldots \frac{1}{2n} = H_{2n}-\frac{1}{2}H_n
$$
and each $H_{k} \sim \log k +\gamma$.
EDIT: Since $H_{2n} \sim \log 2n + \gamma = \log 2 + \log n + \gamma$ this whole expression reduces to $\frac{1}{2} \log n +\log 2 +\frac{\gamma}{2}$
