  Various limit-free formulas are given for the computation of the algebraic
and the topological entropy, respectively in the settings of endomorphisms of
locally finite discrete groups and of continuous endomorphisms of totally
disconnected compact groups. As applications we give new proofs of the
connection between the algebraic and the topological entropy in the abelian
case and of the connection of the topological entropy with the finite depth for
topological automorphisms.
