| Exam Board | SPS |
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| Module | SPS SM Pure (SPS SM Pure) |
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| Year | 2024 |
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| Session | September |
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| Topic | Geometric Sequences and Series |
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9. The sum to infinity of the geometric series
$$a + a r + a r ^ { 2 } + \ldots$$
is 10 .
The sum to infinity of the series formed by the squares of the terms is 100/9.
a) Show that \(r = 4 / 5\) and find \(a\).
b) Find the sum to infinity of the series formed by the cubes of the terms.
\section*{(Total for Question 9 is 5 marks)}