We define a perfect ternary tree of height h as a tree where the distances (number of edges) from every leaf to the root is exactly h, and every non-leaf node has exactly 3 children. Prove by induction that for every h = 1,2,..., the number of leaves in such a tree is 3h, and the number of nodes in total is 21 (3h+1 1).

We define a perfect ternary tree of height h as a tree where the distances (number of edges) from every leaf to the root is exactly h, and every non-leaf node has exactly 3 children. Prove by induction that for every h = 1,2,..., the number of leaves in such a tree is 3", and the number of nodes in total is 1 (3+1 1)