How to count to 7

Looking at Pascal's Triangle , we see that we must find the sum of the sums of rows 0-7 of it. We recall that the sum of numbers in the $n^{\text{th}}$ row of Pascal's Triangle (starting from $0$ ) is $2^n$ , thus, our answer is $2^0 + 2^1 + 2^2 + \cdots + 2^7$ . We now recall that the sum of the first $n$ powers of two (starting from $2^0$ ) is $2^{n+1} - 1$ . Thus, the answer is $2^8 - 1 = 256-1=\boxed{255}$