Prove any binary tree with $n$ nodes has at least $1+\log_2 n$ levels Prove that any binary tree with $n$ nodes has at least $1+\log_2 n$ levels.
I tried setting $n=8$ and plugging in $8\geq\log_2 8 = 8\geq 3$. But I'm not sure how I can prove this by induction.
Hint: A binary tree with $1+h$ levels contains at most $1+2+2^2+\cdots+2^h = 2^{h+1}-1$ vertices.