| Exam Board | AQA |
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| Module | Further Paper 2 (Further Paper 2) |
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| Year | 2023 |
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| Session | June |
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| Topic | Sequences and series, recurrence and convergence |
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7 Show that
$$\sum _ { r = 11 } ^ { n + 1 } r ^ { 3 } = \frac { 1 } { 4 } \left( n ^ { 2 } + a n + b \right) \left( n ^ { 2 } + a n + c \right)$$
where \(a\), \(b\) and \(c\) are integers to be found.
\(8 \quad \mathbf { A }\) is a non-singular \(2 \times 2\) matrix and \(\mathbf { A } ^ { \mathrm { T } }\) is the transpose of \(\mathbf { A }\)