  We show how to get explicit induction formulae for finite group
representations, and more generally for rational Green functors, by summing a
divergent series over Dwyer's subgroup and centralizer decomposition spaces.
This results in formulae with rational coefficients. The former space yields a
well-known induction formula, the latter yields a new one. As essentially
immediate corollaries of the existing literature, we get similar formulae in
group cohomology and stable splittings of classifying spaces.
