Problem 5.29. (Fibonacci trees) It is convenient to define the Fibonacci tree F-1 to consist of a single node. Then the i-th Fibonacci tree Fi,i 2 0, is defined recursively to consist of a root node with i children, where the j-th child, 1 s j s i, is in turn the root of a Fibonacci tree Fj-2. Figure 5.23 shows Fo to F5. Prove that the Fibonacci tree Fi, i 2 0, has fi 2 nodes, where fk is the k-th member of the Fibonacci sequence; see Section 1.6.4. Fo F F2 F3 F4 Figure 5.23. Fibonacci trees Fo to F4