Russia | Math Olympiad | A Nice Algebra Problem

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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)