Summation (Σ)

The problem, from first principles

Every other track on this site writes formulas using Σ (sigma) without ever teaching what it means — a loss function's Σ_i (y_i - ŷ_i)², entropy's -Σ_x p(x) log p(x), a dot product's Σ_i a_i b_i. All of them are the exact same idea: "add up a sequence of values, one per index, over a specified range." This question makes that idea concrete before it shows up disguised inside a bigger formula.

From theory to code

Σ is nothing more than a for loop that accumulates a running total. Implement summation(f, lo, hi), computing Σ_{i=lo}^{hi} f(i) — call f once per integer i from lo to hi inclusive, and add up the results. The signature and docstring are already in the editor.

Constraints

• lo and hi are integers; hi may be less than lo, in which case the sum is empty (the standard mathematical convention: an empty sum is 0).
• f takes a single integer and returns a number (int or float).
• Do not use sum() with a generator that secretly hides the loop from yourself — write the accumulation explicitly, since the point is to see the mechanics Σ is standing in for.

Hints