AQA
Further AS Paper 1
2021
June
— Question 9
4 marks
Exam Board
AQA
Module
Further AS Paper 1 (Further AS Paper 1)
Year
2021
Session
June
Marks
4
Topic
Sequences and series, recurrence and convergence
9
Use the standard formulae for \(\sum _ { r = 1 } ^ { n } r\) and \(\sum _ { r = 1 } ^ { n } r ^ { 2 }\) to show that
$$\sum _ { r = 1 } ^ { n } r ( r + 3 ) = a n ( n + 1 ) ( n + b )$$
where \(a\) and \(b\) are constants to be determined. [0pt]
[4 marks]
9
Hence, or otherwise, find a fully factorised expression for
$$\sum _ { r = n + 1 } ^ { 5 n } r ( r + 3 )$$
$$\mathbf { A } = \left[ \begin{array} { c c }
3 & i - 1
i & 2
\end{array} \right]$$