Vocabulary - Prefix Sum

A prefix sum array stores cumulative sums. Define $pref[i]$ as the sum of the first $i$ elements: $pref[0] = 0$ $pref[i] = a[1] + a[2] + \ldots + a[i]$ for $i \ge 1$ For example, if $a = [3, 1, 4, 1, 5]$, then $pref = [0, 3, 4, 8, 9, 14]$.

Notice $pref[0] = 0$ is a boundary case. It represents "sum of zero elements." This makes the formula for range sums cleaner, as you'll see next.