Please solve Q6

Example 4.2 {A Communications System) Consider a communications system that transmits the digits 0 and 1. Each digit transmitted must pass through several stages, at each of which there is a probability p that the digit entered will be unchanged when it leaves. Letting Xn denote the digit entering the nth stage, then {Xm n = 0, l, . . .} is a two-state Markov chain having a transition probability matrix 11:\" 1" lp I 1p )9 6. Let the transition probability matrix of a two-state Markov chain be given, as in Example 4.2, by P 1 - P P = 1 - P P Show by mathematical induction that P() _ 2 + = (2p - 1)" (2p - 1)" - =(2p - 1)" N- N- +5(2p - 1)"