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A numerical study of the string tension and of the masses of the lowest-lying glueballs is performed in SU(N)
gauge theories for 2 ≤ N ≤ 8 in D = 3+1 and 2 ≤ N ≤ 6 in D = 2+1. It is shown that for the string
tension a smooth N -> ∞ limit exists that depends only on the 't Hooft coupling λ = g2 N. An
extrapolation of the masses of the lightest glueballs to N = ∞ using a power series in 1/N2
shows that the leading correction to the infinite N value accounts for finite N effects for N at least as small as
3 and all the way down to N = 2 in many cases. k-string tension ratios and possible issues connected with
correlation functions at large N are also discussed.