  Employing higher order perturbation theory, we obtain charged rotating black
holes in odd dimensions, where the Einstein-Maxwell Lagrangian may be
supplemented with a Chern-Simons term. Starting from the Myers-Perry solutions,
we use the electric charge as the perturbative parameter, and focus on extremal
black holes with equal-magnitude angular momenta. For
Einstein-Maxwell-Chern-Simons theory with arbitrary Chern-Simons coupling
constant, we perform the perturbations up to third order for any odd dimension.
We discuss the physical properties of these black holes and study their
dependence on the charge. In particular, we show that the gyromagnetic ratio
$g$ of Einstein-Maxwell black holes differs from the lowest order perturbative
value $D-2$, and that the first correction term to $g/(D-2)$ is universal.
