| Exam Board | Edexcel |
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| Module | PMT Mocks (PMT Mocks) |
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| Topic | Geometric Sequences and Series |
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15. An infinite geometric series has first four terms \(1 - 2 x + 4 x ^ { 2 } - 8 x ^ { 3 } + \cdots\). The series is convergent.
a. Find the set of possible values of \(x\) for which the series converges.
Given that \(\sum _ { r = 1 } ^ { \infty } ( - 2 x ) ^ { r - 1 } = 8\),
b. calculate the value of \(x\).