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Consider a Markov chain on {0,1,2, ...} such that from state i, the chain goes to...

Consider a Markov chain on {0,1,2, ...} such that from state i, the chain goes to i + 1 with probability p, 0 <p <1, and goes to state 0 with probability 1 - p. 
a) Show that this string is irreducible. b) Calculate P0 (T0 = n), n ≥ 1. c) Show that the chain is recurring.
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