| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2013 |
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| Session | November |
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| Topic | Sequences and series, recurrence and convergence |
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3 It is given that
$$S _ { n } = \sum _ { r = 1 } ^ { n } u _ { r } = 2 n ^ { 2 } + n$$
Write down the values of \(S _ { 1 } , S _ { 2 } , S _ { 3 } , S _ { 4 }\). Express \(u _ { r }\) in terms of \(r\), justifying your answer.
Find
$$\sum _ { r = n + 1 } ^ { 2 n } u _ { r } .$$