There are at most 2l nodes at level l.
To Prove: There are at most 2l nodes at level l in a binary tree.
By induction:
Prove true for the base case
At level 0 there are at most 20 = 1
Strong Induction: Assume true for k
At level k there are at most 2k nodes.
Prove for k+1
To show: At level k+ there are at most 2k+1 nodes.
By the inductive step, there are at most 2k nodes at level k.
Since it is a binary tree, each node at level k may have two children, so
there are at most 2*2k nodes at level k+1.
Since 2*2k = 2k+1 the proof is complete.