| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2019 |
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| Session | November |
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| Topic | Proof by induction |
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2 It is given that \(y = \ln ( a x + 1 )\), where \(a\) is a positive constant. Prove by mathematical induction that, for every positive integer \(n\),
$$\frac { \mathrm { d } ^ { n } y } { \mathrm {~d} x ^ { n } } = ( - 1 ) ^ { n - 1 } \frac { ( n - 1 ) ! a ^ { n } } { ( a x + 1 ) ^ { n } }$$