| Exam Board | CAIE |
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| Module | Further Paper 1 (Further Paper 1) |
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| Year | 2020 |
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| Session | November |
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| Topic | Proof by induction |
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5 Prove by mathematical induction that, for every positive integer \(n\),
$$\frac { d ^ { 2 n - 1 } } { d x ^ { 2 n - 1 } } ( x \sin x ) = ( - 1 ) ^ { n - 1 } ( x \cos x + ( 2 n - 1 ) \sin x )$$