| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2011 |
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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 \(n\),
$$\frac { \mathrm { d } ^ { n } } { \mathrm {~d} x ^ { n } } \left( \frac { 1 } { 2 x + 3 } \right) = ( - 1 ) ^ { n } \frac { n ! 2 ^ { n } } { ( 2 x + 3 ) ^ { n + 1 } }$$