| 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 \(n\),
$$1 + 2 x + 3 x ^ { 2 } + \ldots + n x ^ { n - 1 } = \frac { 1 - ( n + 1 ) x ^ { n } + n x ^ { n + 1 } } { ( 1 - x ) ^ { 2 } }$$