2k+1-1 where k >= 1

The maximum number of nodes in a binary tree of height k can be calculated using the formula:

$2^{k + 1} - 1$

This formula represents the maximum number of nodes that can exist in a binary tree of height $k$ . It derives from the fact that each level of a binary tree doubles the number of nodes compared to the previous level. The maximum number of nodes at any level is $2^{h}$ , where $h$ is the height of the tree. Summing up all the nodes from level 0 to level $k$ gives the formula above.

So, the correct answer to the question would be: $2^{k + 1} - 1$ .