what is "geometric'' infinite sum of markov matrix

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 $$I + PM + P^2M^2 + \cdots + P^tM^t + \cdots$$?