Toss a fair die repeatedly. Let [math]S_n[/math] denote the total of the outcomes through the [math]n[/math]th toss. Show that there is a limiting value for the proportion of the first [math]n[/math] values of [math]S_n[/math] that are divisible by 7, and compute the value for this limit. Hint: The desired limit is an equilibrium probability vector for an appropriate seven state Markov chain.