ITPEC FE Subject A October 2024 Question 6

Recursive sum f(n) — compute f(5) for a recursive function.

f(n): if n ≤ 1 return 1, else return n + f(n−1)

• •f(5) = 5 + f(4) = 5 + 4 + f(3) = … = 5 + 4 + 3 + 2 + 1 = 15

This is the classic sum formula: n × (n + 1) / 2 = 5 × 6 / 2 = 15

Why not others:
- (a) 6 — this is f(3) = 3 + 2 + 1
- (b) 9 — this is f(3) + f(2) or a miscalculation
- (d) 25 — confuses with n², i.e. 5 × 5

Key rule: When a recursive function adds n + f(n−1) with base case f(1) = 1, it computes the sum 1 + 2 + … + n.

AI-generated — may contain errors