18. Let $ X(t): t 0 % be a birth and death process with birth rates $ n % n=0 and death rates $

18. Let $ X(t): t ≥ 0 % be a birth and death process with birth rates $ λn %∞ n=0 and death rates $ µn %∞ n=1. Show that if.∞ k=1 µ1µ2 ···µk λ1λ2 ··· λk = ∞, then, with probability 1, eventually extinction will occur.