  Using the effective center model of QCD we test series expansions for finite
chemical potential $\mu$. In particular we study two variants of Taylor
expansion as well as the fugacity series. The effective center model has a dual
representation where the sign problem is absent and reliable Monte Carlo
simulations are possible at arbitrary $\mu$. We use the results from the dual
simulation as reference data to assess the Taylor- and fugacity series
approaches. We find that for most of parameter space fugacity expansion is the
best (but also numerically most expensive) choice for reproducing the dual
simulation results, while conventional Taylor expansion is reliable only for
very small $\mu$. We also discuss the results of a modified Taylor expansion in
$e^{\pm \mu} - 1 $ which at the same numerical effort clearly outperforms the
conventional Taylor series.
