> How many nulls are there in a binary tree of n nodes? Why?

n + 1

Proof by induction.

Base case. n = 1
Tree of one element has two nulls (empty left and right subtrees).
1 + 1 = 2

Step case. Tree T of n elements has n + 1 nulls.
Let's add one more element to the tree. The new element will occupy one of the
nulls, but bring two more (empty left and right subtrees).

n + 1 - 1 + 2 = (n + 1) + 1

Qed.