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Home » But this contradicts intuition — is it really 56.25%? - go-checkin.com

But this contradicts intuition — is it really 56.25%? - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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Letâs write $ a = rac{20}{r^{1.5}} $. Substitute into the sum:
rac{20}{r^{1.5}} (1 + r + r^2 + r^3) = 120
\Rightarrow rac{20(1 + r + r^2 + r^3)}{r^{1.5}} = 120
\Rightarrow rac{1 + r + r^2 + r^3}{r^{1.5}} = 6
Try $ r = 1 $:
rac{1 + 1 + 1 + 1}{1} = 4 < 6
Try $ r = 2 $:
rac{1 + 2 + 4 + 8}{2^{1.5}} = rac{15}{2\sqrt{2}} pprox rac{15}{2.82...
Try $ r = 3 $:
rac{1 + 3 + 9 + 27}{3^{1.5}} = rac{40}{3\sqrt{3}} pprox rac{40}{5.1...

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