Prove that the acceptance/rejection method works for discrete distributions. That is, let f and g be p.f.s

Question:

Prove that the acceptance/rejection method works for discrete distributions. That is, let f and g be p.f.’s rather than p.d.f.’s, but let the rest of the acceptance/rejection method be exactly as stated. The proof can be translated by replacing integrals over x by sums. Integrals over u should be left as integrals.