| Exam Board | OCR |
|---|---|
| Module | FP1 AS (Further Pure 1 AS) |
| Year | 2021 |
| Session | June |
| Marks | 5 |
| Topic | Proof by induction |
| Type | Prove inequality: factorial/exponential |
| Difficulty | Standard +0.3 This is a straightforward proof by induction with a clear base case (n=9) and a standard inductive step requiring the inequality 2^(2n+2) < (n+1)·2^(2n), which simplifies to showing 4 < n+1 for n≥9. While it requires understanding of induction structure and factorial manipulation, it follows a completely standard template with no conceptual surprises, making it slightly easier than average for an A-level Further Maths question. |
| Spec | 4.01a Mathematical induction: construct proofs |
4 Prove that $n ! > 2 ^ { 2 n }$ for all integers $n \geqslant 9$.
\hfill \mbox{\textit{OCR FP1 AS 2021 Q4 [5]}}