Stationary distribution of countable Markov chain

[shoplifter]

How do I find the stationary distribution of the Markov chain with the countable state space {0, 1, 2, ..., n, ...}, where each point, including 0, can either

a. return to 0 with probability 1/2, or
b. move to the right n -> n+1 with probability 1/2?

Thanks.

 

[Eynstone]

Prob. of state n = (1/2)^(n+1). This is obtained by calculation of steady state of
{0,1,..n} and letting n -> infinity.