sum: O(n), get sum of segment: O(1)

prefixed-sum.js

function prefixedSum(array) {
  const sum = new Array(array.length + 1)
  sum[0] = 0

  for(let k = 1; k < sum.length; k++) {
    sum[k] = (sum[k - 1] || 0) + array[k - 1]
  }

  return sum  
}

function segmentSum(sum, x, y) {
  return sum[y + 1] - sum[x]
}