| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Proof by induction |
| Type | Prove divisibility |
| Difficulty | Standard +0.3 This is a straightforward proof by induction with a divisibility statement. The base case is trivial (f(1) = 20), and the inductive step requires standard algebraic manipulation to show f(k+1) - f(k) is divisible by 4, using 7^(k+1) = 7ยท7^k. While it's Further Maths content, it follows a completely standard template with no conceptual surprises, making it slightly easier than average overall. |
| Spec | 4.01a Mathematical induction: construct proofs |
$$f(n) = (2n + 1)7^n - 1.$$
Prove by induction that, for all positive integers $n$, $f(n)$ is divisible by 4.
[6]
\hfill \mbox{\textit{Edexcel FP1 Q14 [6]}}