| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2004 |
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| Session | November |
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| Topic | Sequences and series, recurrence and convergence |
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5 Let
$$S _ { N } = \sum _ { n = 1 } ^ { N } ( - 1 ) ^ { n - 1 } n ^ { 3 }$$
Find \(S _ { 2 N }\) in terms of \(N\), simplifying your answer as far as possible.
Hence write down an expression for \(S _ { 2 N + 1 }\) and find the limit, as \(N \rightarrow \infty\), of \(\frac { S _ { 2 N + 1 } } { N ^ { 3 } }\).