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TR-MO-R1 2015 Problem 3

    1,12,14,18,…1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \dots sonsuz geometrik dizisinin bazı elemanları silinerek toplamı SS ye eşit olan bir sonsuz geometrik dizi elde edilebiliyorsa, SS sayısı 12015,1215,115,15\frac{1}{2015}, \frac{1}{215}, \frac{1}{15}, \frac{1}{5} değerlerinden kaçına eşit olabilir?

    a) 0 b) 1 c) 2 d) 3 e) 4

    Official text Turkish Mathematical Olympiad, first round 2015 official paper, page 2. Quoted with source.

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