AQA
Further AS Paper 1
Specimen
— Question 10
8 marks
Exam Board
AQA
Module
Further AS Paper 1 (Further AS Paper 1)
Session
Specimen
Marks
8
Topic
Proof by induction
10
Prove that
$$6 + 3 \sum _ { r = 1 } ^ { n } ( r + 1 ) ( r + 2 ) = ( n + 1 ) ( n + 2 ) ( n + 3 )$$
[6 marks]
10
Alex substituted a few values of \(n\) into the expression \(( n + 1 ) ( n + 2 ) ( n + 3 )\) and made the statement:
"For all positive integers n,
$$6 + 3 \sum _ { r = 1 } ^ { n } ( r + 1 ) ( r + 2 )$$
is divisible by \(12 . "\)
Disprove Alex's statement. [0pt]
[2 marks]