| Exam Board | SPS |
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| Module | SPS FM (SPS FM) |
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| Year | 2020 |
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| Session | December |
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| Topic | Proof by induction |
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13. A series is given by
$$\sum _ { r = 1 } ^ { k } 9 ^ { r - 1 }$$
i. Write down a formula for the sum of this series.
ii. Prove by induction that \(P ( n ) = 9 ^ { n } - 8 n - 1\) is divisible by 64 if \(n\) is a positive integer greater than 1 .
Spare space for extra working.
Spare space for extra working.