| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2017 |
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| Session | June |
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| Marks | 6 |
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| Topic | Proof by induction |
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3 Prove, by mathematical induction, that \(\sum _ { r = 1 } ^ { n } r \ln \left( \frac { r + 1 } { r } \right) = \ln \left( \frac { ( n + 1 ) ^ { n } } { n ! } \right)\) for all positive integers \(n\). [6]