OCR Further Pure Core 1 2021 June — Question 5 5 marks

Exam BoardOCR
ModuleFurther Pure Core 1 (Further Pure Core 1)
Year2021
SessionJune
Marks5
TopicProof by induction
TypeProve by exhaustion (cases)
DifficultyStandard +0.3 This is a straightforward induction proof with a simple divisibility statement. The algebra is routine (expanding (n+1)³ + (n+2)³ + (n+3)³ and showing divisibility by 9), requiring only basic manipulation and factoring. While it's a Further Maths question, it's a standard template application of induction with no novel insight needed, making it slightly easier than average.
Spec1.01a Proof: structure of mathematical proof and logical steps

5 Prove by induction that the sum of the cubes of three consecutive positive integers is divisible by 9 .

5 Prove by induction that the sum of the cubes of three consecutive positive integers is divisible by 9 .

\hfill \mbox{\textit{OCR Further Pure Core 1 2021 Q5 [5]}}