| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2018 |
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| Session | June |
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| Topic | Proof by induction |
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2 It is given that \(\mathrm { f } ( n ) = 2 ^ { 3 n } + 8 ^ { n - 1 }\). By simplifying \(\mathrm { f } ( k ) + \mathrm { f } ( k + 1 )\), or otherwise, prove by mathematical induction that \(\mathrm { f } ( n )\) is divisible by 9 for every positive integer \(n\).