Recomputing range sums per query

An analytics endpoint answers q = 10⁵ queries of the form "sum of values[l..r]" over an array of n = 10⁵ daily totals. It is too slow. Then a second requirement lands: values can also be updated between queries. Optimize both versions.

1def range_sums(values, queries):
2    out = []
3    for l, r in queries:
4        out.append(sum(values[l:r + 1]))
5    return out

1. State the current worst-case cost and what structure of the work is repeated across queries.
2. Give an O(n) preprocessing / O(1) per query solution for the read-only case.
3. Explain why that solution breaks when a single value is updated, and what the cost of maintaining it would be.
4. Propose a structure that supports both point updates and range sums in O(log n) and sketch its operations.
5. Discuss when a plain prefix array is still the right choice despite updates.