| Exam Board | SPS |
|---|
| Module | SPS FM Pure (SPS FM Pure) |
|---|
| Year | 2021 |
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| Session | September |
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| Topic | Proof by induction |
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9.
The sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by
$$u _ { 1 } = 2 , \quad u _ { n + 1 } = \frac { 5 u _ { n } - 3 } { 3 u _ { n } - 1 }$$
Prove by induction that, for all integers \(n \geqslant 1\),
$$u _ { n } = \frac { 3 n + 1 } { 3 n - 1 }$$
(6 marks)
[0pt]
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