| Exam Board | OCR |
|---|---|
| Module | FP1 AS (Further Pure 1 AS) |
| Year | 2017 |
| Session | Specimen |
| Marks | 5 |
| Topic | Proof by induction |
| Type | Prove inequality: factorial/exponential |
| Difficulty | Standard +0.8 This is a straightforward proof by induction on a standard inequality, requiring students to establish a base case (n=4) and complete an inductive step. While it's a Further Maths topic and requires understanding of proof technique, the algebraic manipulation in the inductive step is relatively simple (multiplying by (k+1) and showing (k+1) > 2 for k≥4), making it a routine FP1 induction question rather than one requiring significant insight. |
| Spec | 4.01a Mathematical induction: construct proofs |
Prove that $n! > 2^n$ for $n \geq 4$. [5]
\hfill \mbox{\textit{OCR FP1 AS 2017 Q8 [5]}}