TR-MO-R1 2019 Problem 19

$x=\dfrac{8}{(16+\sqrt{240})(4+\sqrt[4]{240})(2+\sqrt[8]{240})}$ olmak üzere, $\dfrac{1}{1-(1-x)^8}$ kaçtır?

a) 2 b) 4 c) 8 d) 16 e) 64

Official text Turkish Mathematical Olympiad, first round 2019 official paper, page 10. Quoted with source.

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