AR(p) process is denoted by: $X_t=\mu+\alpha_1(X_{t-1}-\mu)+\alpha_2(X_{t-2}-\mu)+...\alpha_p(X_{t-p}-\mu)$

I don't understand forecast error.
Let $\epsilon_{t+l}$ be the forecast error t $l$ step ahead forecast .
Then it says that it can be shown that
$\epsilon _{t+l}=Z_{t+l}+\alpha_1Z_{t+l-1}+\alpha_1^2Z_{t+l-2}+....+\alpha_1^{l-1}Z_{t+1}$
How is this obtained?

My second question is for a MA(1) process it is obtained that
$V(\hat \epsilon_{t+1})=\hat\sigma^2 $ ; if $l=1$
$V(\hat \epsilon_{t+1})=\hat\sigma^2 (1+\beta_1^2)$ ; if $l>=2$

Can someone please tell me the method as to how these errors were obtained.

AR(p) process is denoted by: $X_t=\mu+\alpha_1(X_{t-1}-\mu)+\alpha_2(X_{t-2}-\mu)+...\alpha_p(X_{t-p}-\mu)+Z_t$

I don't understand forecast error.
Let $\epsilon_{t+l}$ be the forecast error at $l$ step ahead forecast .
Then it says that it can be shown that
$\epsilon _{t+l}=Z_{t+l}+\alpha_1Z_{t+l-1}+\alpha_1^2Z_{t+l-2}+....+\alpha_1^{l-1}Z_{t+1}$
How is this obtained?

My second question is for a MA(1) process it is obtained that
$V(\hat \epsilon_{t+1})=\hat\sigma^2 $ ; if $l=1$
$V(\hat \epsilon_{t+1})=\hat\sigma^2 (1+\beta_1^2)$ ; if $l>=2$

Can someone please tell me the method as to how these errors were obtained.