What is the maximum number of nodes in a binary tree of height k?

Software Development
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#1

What is the maximum number of nodes in a binary tree of height k?

#2

Since the given height of tree is k, and we also know that a binary tree can contain maximum two nodes in one level, hence we can have a total of 2^k nodes.

#3

Height 1: 1 node=21−1=21−1

Height 2: 1+2 nodes=22−1=22−1

Height 3: 1+2+4 nodes=23−1=23−1

So the general pattern is height h=2ℎ−1=2h−1 nodes.