Maths Olympiad Prep

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, 1999

Algebra Difficulty 3.0 AMC 10/12 Find the answer Canada

If a1=11xa_1 = \frac{1}{1-x}, a2=11a1a_2 = \frac{1}{1-a_1}, and an=11an1a_n = \frac{1}{1-a_{n-1}}, for n2n \ge 2, x1x \ne 1 and x0x \ne 0, then a107a_{107} is

(A) 11x\frac{1}{1-x} (B) xx (C) x-x (D) x1x\frac{x-1}{x} (E) 1x\frac{1}{x}

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.