Prefix Sums - Implementation

function buildPrefix(a, n)
    pref[0] := 0
    for i from 1 to n
        pref[i] := pref[i-1] + a[i]
    return pref

function rangeSum(pref, l, r)
    return pref[r] - pref[l-1]

Watch the indexing. If your array is $0$-indexed, adjust the formula to $pref[r+1] - pref[l]$. Off-by-one errors are the most common bug here. Trace through a small example by hand before submitting.

Time complexity: $O(n)$ to build, $O(1)$ per query.

Space complexity: $O(n)$ for the prefix array.