It's pretty clear what the pattern is - 2^(k-1) * (-1)^(k-1) would work backwards, but we have to work forwards to get lower in this case, so we could start at -3 (as long as we put the k-1 in absolute value to make sure it's not 1/8), so we could write it as ∑ (k=1, goes to 4) 2^(|k-4|)*(-1)^(k-4)
It doesn't matter for k-4 because 1/-1 and 1/1 are the same thing as -1 and 1 respectively