OCR FP1 AS 2017 Specimen — Question 8 5 marks

Exam BoardOCR
ModuleFP1 AS (Further Pure 1 AS)
Year2017
SessionSpecimen
Marks5
TopicProof by induction
TypeProve inequality: factorial/exponential
DifficultyStandard +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.
Spec4.01a Mathematical induction: construct proofs

Prove that \(n! > 2^n\) for \(n \geq 4\). [5]

Prove that $n! > 2^n$ for $n \geq 4$. [5]

\hfill \mbox{\textit{OCR FP1 AS 2017 Q8 [5]}}