| Exam Board | Edexcel |
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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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2. (a) Show, using the formulae for \(\sum r\) and \(\sum r ^ { 2 }\), that
$$\sum _ { r = 1 } ^ { n } \left( 6 r ^ { 2 } + 4 r - 1 \right) = n ( n + 2 ) ( 2 n + 1 )$$
(b) Hence, or otherwise, find the value of \(\sum _ { r = 11 } ^ { 20 } \left( 6 r ^ { 2 } + 4 r - 1 \right)\).