# graph theory proof

#### mathh18

A binary tree of height h is called a complete binary tree if it is either empty, or it has two complete subtrees both of height h-1. Prove by induction on n greater than or equal to 0, that a complete binary tree with height n has 2^(n-1) total nodes

#### roninpro

Are you sure the statement of your problem is correct?

When $$\displaystyle n=1$$, your tree has three nodes, which contradicts the formula you have given.