Range Sum - Prefix Sum Idea

Create an array $prefix$ where $prefix[i]$ is the sum of all elements from index $0$ to $i$. This is a cumulative sum.

For $nums = [-2, 0, 3, -5, 2, -1]$, compute $prefix = [-2, -2, 1, -4, -2, -3]$. Each entry adds the current element to the previous sum.

To find the sum from $i$ to $j$, compute $prefix[j] - prefix[i-1]$ (or just $prefix[j]$ if $i = 0$). This uses the telescoping property: intermediate terms cancel.