| Exam Board | OCR MEI |
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| Module | Further Pure Core AS (Further Pure Core AS) |
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| Year | 2021 |
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| Session | November |
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| Topic | Proof by induction |
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5 Prove by induction that \(\sum _ { r = 1 } ^ { n } r \times 2 ^ { r - 1 } = 1 + ( n - 1 ) 2 ^ { n }\) for all positive integers \(n\).