Notice that the sum of the powers of $2$ from $1$, which is $2^0$, to $2^{n-1}$ is equal to ${2^n}{-1}$. Please explain in quotations!
"Notice that the sum of the powers of $2$ from $1$, which is $2^0$, to $2^{n-1}$ is equal to $2^n-1$." In a very simple case, for $n = 3, 1 + 2 + 4 = 7 = 8 - 1$.

If you’re familiar with binary, simply note that
$$2^n-1 = {1\underbrace{000\dots00}_{\text{$n$ zeros}}}\text{$_2$} - 1 = \underbrace{111\dots11}_{\text{$n$ ones}}\text{$_2$}$$
