| Exam Board | OCR |
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| Module | Further Pure Core 1 (Further Pure Core 1) |
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| Session | Specimen |
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| Topic | Proof by induction |
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9 Prove by induction that, for all positive integers \(n\),
$$\sum _ { r = 1 } ^ { n } \frac { 5 - 4 r } { 5 ^ { r } } = \frac { n } { 5 ^ { n } }$$