TITLE: The maximum number of nodes in a binary tree of depth $k$ is $2^{k}-1$, $k \geq1$.
QUESTION [22 upvotes]: I am confused with this statement
The maximum number of nodes in a binary tree of depth $k$ is $2^k-1$, $k \geq1$.
How come this is true. Lets say I have the following tree
    1
   / \
  2   3

Here the depth of the tree is 1. So according to the formula, it will be $2^1-1 = 1$. But we have $3$ nodes here. I am really confused with this depth thing. 
Any clarifications?

REPLY [5 votes]: You answer yourself in the question.
The number of nodes is equal to $2^{k}-1$ where $k≥1$. So the minimum level is 1, not 0. 
Thus the example is correct because it has 2 levels of depth: $2^{2}-1 = 3$