Discrete Math and Statistics: Auto Regressive (AR) Formula

1. Can
Var(X_n) = (a^(2n – 2) + A^(2n – 4) + … + A^2 + 1)sigma^2, be written as[
(sigma^2 )*(SUM(A2)n)from A=0 to A=n-1 =(sigma^2 )*(1/(1- A2 ) if n is large?

2. Why does
Cov (Xi,Xj) = 0 if i /= j and sigma^2 if i=j

3. What is
the basic equation for the Covariance?

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