I am reading the Wiley's Multivariate Time Series Analysis Book and there is an step that I don't understand.

At pag. 18 it gets the following equation:

$\mu = c + \sum_{i=1}^{\infty} \pi_i \mu$

where $\mu$ is a column vector of size $k$ and $c$ and $\pi_i$ are matrices of size $k$x$k$.

Then it says:

Letting $\pi_0 = I_k$, we obtain, from the prior equation,

$\Big( \sum_{i=0}^{\infty} \pi_i \Big) \mu = c$.

And I don't know how it gets there...I suppose it is a very simple step but I don't see it.

I'd appreciate if someone can explain it.

Thank you!!


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