N[2^(1/3)-Sqrt[1+1/2Sqrt[1+1/3Sqrt[1+1/4Sqrt[1+GoldenRatio/5]]]],{Infinity,20}]N[2^(1/3)-Sqrt[1+1/2Sqrt[1+1/3Sqrt[1+1/4Sqrt[1+GoldenRatio/5]]]],{Infinity,20}]

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