Consider a quantum system with an infinite number of states. The n state is occupied with a probability Pn, given by, Pp = 19 for n = 1, 2, .... (a) Show that the probability distribution is normalized. (b) The entropy is given in terms of the state probabilities p, by S = -k> Pn In Pn. n=1 where & is Boltzmann's constant. Calculate the entropy of the system. (Hint: To do part (a) recall the value of the geometric series _, a" = (1-x)- For part (b) consider what happens if the geometric series is differentiated with respect to c.)