| Exam Board | CAIE |
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| Module | Further Paper 1 (Further Paper 1) |
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| Year | 2023 |
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| Session | November |
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| Topic | Proof by induction |
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2 Prove by mathematical induction that, for all positive integers \(n\),
$$\frac { d ^ { n } } { d x ^ { n } } \left( x ^ { 2 } e ^ { x } \right) = \left( x ^ { 2 } + 2 n x + n ( n - 1 ) \right) e ^ { x }$$