Assume a proper and complete binary tree $T$ with $n>1$ nodes. Let $E(T)$ represent the sum of the depths of all external nodes in $T$, and $I(T)$ represent the sum of the depths of all internal nodes in $T$. Prove that:
$E(T) = O(n⋅\log n)$
To prove this that it is equal to $E(T)$, do I just go plug in numbers till I get the exact $E(T)$ given? I can't figure this out, can someone help?