 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ia/paper-4/5e/a/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

(r n)

as the number of

r

-element subsets of an

n

-element set, equivalently as

n! / [r! (n - r)!]

. Partitioning the

r

-element subsets of

{1, \dots, n + 1}

according to whether they contain

n + 1

(r n + 1) = (r n) + (r - 1 n) .

(δ f_{r}) (n) = (r n + 1) - (r n) = (r - 1 n) = f_{r - 1} (n) .

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