So, I have this function: $$ y_t=v_t+\rho v_{t-1}+\rho^2 v_{t-2}+\dots+\rho^{t-1}v_1+\rho^ty_0 $$
And I want to find the variance (and after that the covariance, but I should be able to do that..). I know that the variance is: $ Var[y_t]=\frac{var[v]}{1-\rho^2}=\frac{\sigma^2_v}{1-\rho^2} $
But somewhere I mess everything up : (