Maximum Nodes

nodes(h)	=	leaves(h) + nodes(h-1)
	=	2h + nodes(h-1)
	=	2h + 2h-1 + nodes(h-2)
	=	2h + 2h-1 + 2h-2 + ... + 4 + 2 + 1

Now rewrite nodes(h) as (2 x nodes(h)) - nodes(h):

2 x nodes(h)	= 2h+1	+	2h + 2h-1 + 2h-2 + ... + 4 + 2
− nodes(h)	=	−	2h − 2h-1 − 2h-2 − ... − 4 − 2 − 1
nodes(h)	= 2h+1 − 1

Exercise 8.10: Prove that nodes(h) = 2^h+1 − 1 by induction on h.