Consider a time-invariant Markov chain on the state-space {0, 1, 2, ..., i, i+1, ...} comprising the nonnegative integers. Suppose that the transition probabilities are P(i, i+1) = A for i ≥ 0, and P(i, i-1) = B for i ≥ 1, where A + B = 1. Also, let p(0) = 0. Consider a linear Lyapunov function V(i) and use Foster's Theorem to show that the Markov chain is positive recurrent.