Nested Cuberoots

Algebra Level 5

Compute:

54+972+21870+551124+14526054+33333 \sqrt[3]{54+\sqrt[3]{972+\sqrt[3]{21870+\sqrt[3]{551124+\sqrt[3]{14526054+\cdots}}}}}

Details and assumptions: nth n^\text{th} term is given by 27n+32n+1 27^n + 3^{2n+1} .

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