For the transition matrix P = [0.8 2 0.2 2, 0.3 0.7], solve the equation SP = S to find the stationary matrix S and the limiting matrix Upper P overbar.

Use the ratio test to determine whether ∑n=14∞n+2n! converges or diverges. (a) find the ratio of successive terms. write your answer as a fully simplified fraction. for n≥14, limn→∞∣∣∣an+1an∣∣∣=limn→∞.