  We have carried out extensive series studies, at T=0 and at high
temperatures, of 2-chain and 3-chain spin-half ladder systems with
antiferromagnetic intrachain and both antiferromagnetic and ferromagnetic
interchain couplings. Our results confirm the existence of a gap in the 2-chain
Heisenberg ladders for all non-zero values of the interchain couplings.
Complete dispersion relations for the spin-wave excitations are computed. For
3-chain systems, our results are consistent with a gapless spectrum. We also
calculate the uniform magnetic susceptibility and specific heat as a function
of temperature. We find that as $T\to 0$, for the 2-chain system the uniform
susceptibility goes rapidly to zero, whereas for the 3-chain system it
approaches a finite value. These results are compared in detail with previous
studies of finite systems.
