| Exam Board | Edexcel |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Session | Specimen |
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| Topic | Sequences and series, recurrence and convergence |
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5. (a) Show that \(\sum _ { r = 1 } ^ { n } \left( r ^ { 2 } - r - 1 \right) = \frac { 1 } { 3 } ( n - 2 ) n ( n + 2 )\).
(b) Hence calculate the value of \(\sum _ { r = 10 } ^ { 40 } \left( r ^ { 2 } - r - 1 \right)\).