I have a book series of time and says in part:

An example of time series would be:

$\displaystyle Y_t = 0.8Y_{t -1} + \epsilon_t,$ $\displaystyle t = 1, 2 ...$

Then they say, this series can also be expressed as:

$\displaystyle Y_t = \displaystyle\sum_{i=1}^t{0.8^{t - i}} \epsilon_i$

How do they do and why they develop the series?

Thank you very much.

Greetings.

Dogod