SU(N) gauge theories for all N in 3 and 4 dimensions

We compare the mass spectra and string tensions of SU(2), SU(3) and SU(4) gauge theories in 2+1 dimensions. We find that the ratios of masses are, to a first approximation, independent of N and that the remaining dependence can be accurately reproduced by a simple O(1/N^2) correction. This provides us with a prediction of these mass ratios for all SU(N) theories in 2+1 dimensions and demonstrates that these theories are `close' to N=\infty for N\geq 2. We also find that, when expressed in units of the dynamical length scale of the theory, the dimensionful coupling g^2 is proportional to 1/N at large N. We confirm that these theories are indeed confining in the limit N \to \infty. We describe preliminary calculations in 3+1 dimensions which indicate that the same will be true there.