17. For the random walk of Example 4.19 use the strong law of large numbers to give another proof that the Markov chain is transient when .

Hint: Note that the state at time n can be written asI mage where the Image are independent andI mage. Argue that if , then, by the strong law of large numbers, as and hence the initial state 0 can be visited only finitely often, and hence must be transient. A similar argument holds when .