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If $M$ is a row-normalised Markov matrix, $I$ is an identity matrix, $P=\text{diag}([p_1,\cdots,p_n])$ is a diag matrix and satisfies $p_i\in(0,1)$. When $t\rightarrow \infty$, what is the convergence limit of $I + PM + P^2M^2 + \cdots + P^tM^t + \cdots$?

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