Consider a discreet time series / stochastic process -

x_t = \rho x_{t-1} + \epsilon_t

where \epsilon_t is white noise i.e. iid ~ N(0,\sigma^2)

I need to to prove this series is weak stationary when |\rho| < 1

Definition of weak stationary, I have/use
1. E(x_t) = constant, \mu (independent of t)
2. E(x_t.x_{t+k}) = f(k) i.e. independent of t, it is just a function of lag period, k.

I know this is a pretty basic question, but not really able to go ahead here. Can anyone please help with pointers, references, outline of the proof. Thanks