Fibonacci trees are defined as follows: F-1, F, are a root consisting of a single node. Fi is a root with exactly one child. . For i > 2, F; is defined recursively as follows: F; consist of a root with i children, where the jth child (1 Sisi) is in turn the root of Fibonacci tree Fj-2. (a) Draw Fo, ... F4. (b) Prove that the Fibonacci tree F; (i > 0) has fiti nodes, where fx is the the Fibonacci sequence. (The Fibonacci sequence is defined as fo = 1, fi = 1, fk = fk-1 + fx-2, k > 2. Note that we use fo = 1 here.). Fibonacci trees are defined as follows: F-1, F, are a root consisting of a single node. Fi is a root with exactly one child. . For i > 2, F; is defined recursively as follows: F; consist of a root with i children, where the jth child (1 Sisi) is in turn the root of Fibonacci tree Fj-2. (a) Draw Fo, ... F4. (b) Prove that the Fibonacci tree F; (i > 0) has fiti nodes, where fx is the the Fibonacci sequence. (The Fibonacci sequence is defined as fo = 1, fi = 1, fk = fk-1 + fx-2, k > 2. Note that we use fo = 1 here.)