What is the maximum number of nodes that a binary tree can have at level n? Prove your answer by using mathematical induction. Use this fact to do the following:
a. Rewrite the formal definition of a complete tree of height h.
b. Derive a closed form for the formula.
![376_7aac1d7d-e739-4695-a449-0ac4169d4a4b.png](https://secure.tutorsglobe.com/CMSImages/376_7aac1d7d-e739-4695-a449-0ac4169d4a4b.png)
What is the significance of this sum?