| Exam Board | OCR |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2011 |
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| Session | January |
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| Topic | Proof by induction |
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3 The sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by \(u _ { 1 } = 2\), and \(u _ { n + 1 } = 2 u _ { n } - 1\) for \(n \geqslant 1\). Prove by induction that \(u _ { n } = 2 ^ { n - 1 } + 1\).