| Exam Board | OCR MEI |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2009 |
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| Session | January |
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| Topic | Sequences and Series |
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6 Using the standard results for \(\sum _ { r = 1 } ^ { n } r\) and \(\sum _ { r = 1 } ^ { n } r ^ { 3 }\) show that
$$\sum _ { r = 1 } ^ { n } r \left( r ^ { 2 } - 3 \right) = \frac { 1 } { 4 } n ( n + 1 ) ( n + 3 ) ( n - 2 ) .$$