| Exam Board | OCR |
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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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1 Use formulae for \(\sum _ { r = 1 } ^ { n } r\) and \(\sum _ { r = 1 } ^ { n } r ^ { 2 }\) to show that
$$\sum _ { r = 1 } ^ { n } r ( r + 1 ) = \frac { 1 } { 3 } n ( n + 1 ) ( n + 2 )$$