The maximum number of nodes in a binary tree of depth $k$ is $2^{k}-1$, $k \geq1$. 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?

We assume that the root of a binary tree is on level 1, so in your mentioned tree, the depth is 2 not 1, so (2 to the power 2 ) - 1 = 3 nodes.
