Russia | Math Olympiad | A Nice Algebra Problem
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Пікірлер: 3
Ez
Sₙ = a(rⁿ - 1)/(r - 1) where Sₙ = a + ar + ar² + ... ar⁽ⁿ⁻¹⁾ Let n = 3, a = 2¹¹ and r = 2¹¹ So, S₃ = 2¹¹(2³³ - 1)/( 2¹¹ - 1) = 2¹¹ + 2²² + 2³³ So, S₃/(2³³ - 1) = 2¹¹/(2¹¹ - 1) So, (2¹¹ + 2²² + 2³³)/(2³³ - 1) = 2¹¹/(2¹¹ - 1)