Power series of $\ln\frac{k}{k-1}$ In "Concrete Mathematics", equation (6.63) says that $\ln\frac{k}{k-1}$ expands to the infinite series:
$$
\ln\frac{k}{k-1}=\frac{1}{k} + \frac{1}{2k^2}+\frac{1}{3k^3}+\cdots
$$
But I couldn't see why it can expand in such a way.

Thanks for the quick comments, somtimes I just couldn't see such fundamental things...
$$
\begin{align}
\ln\frac{k}{k-1} &= -\ln\frac{k-1}{k}  \\
&= - \ln\left({1-\frac{1}{k}}\right) \\
&= -\left(-\frac{1}{k}-\frac{1}{2k^2}-\frac{1}{3k^3} - \cdots\right) \\\\
&= \frac{1}{k} + \frac{1}{2k^2}+\frac{1}{3k^3} + \cdots
\end{align}
$$
