c) A Cayley tree is a symmetric regular tree in which each node is connected to the same number k of others, until we get out to the leaves, like this: (We have k = 3 in this picture.) Show that the number of nodes reachable in d steps from the central node is k(k 1)d-1 for d > 1. Hence find an expression for the diameter of the network in terms of k and the number of nodes n