| Exam Board | AQA |
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| Module | Further Paper 2 (Further Paper 2) |
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| Year | 2020 |
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| Session | June |
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| Topic | Proof by induction |
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10 The sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by
$$u _ { 1 } = 0 \quad u _ { n + 1 } = \frac { 5 } { 6 - u _ { n } }$$
Prove by induction that, for all integers \(n \geq 1\),
$$u _ { n } = \frac { 5 ^ { n } - 5 } { 5 ^ { n } - 1 }$$