Variance of Autoregressive models, AR(1)


I'm in high school writing an exam porject in which i have to present tommorow.
There is a proof of how you can calculate variance in an AR(1) mode that I just can't seem to understand. Could anyone please ELI5? Thank you so much.

So, my question is:


Where does the formula derive from? The long one, and how does it turn into the one under with the 0'es?

Thanks again


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  • Hi, I will indeed offer a higher tip in the future. Your answer is amazing. Just a question. Your link doesn't seem to work?

    • I fixed the hyperlink. Sorry about that.

  • Nevermind. It works now. Thanks again

The answer is accepted.