Family of 3's

Level 2

3 32 33 a4a3a2a1= ?\large \sqrt[a_1]{3 \ \sqrt[a_2]{3^2 \ \sqrt[a_3]{3^3 \ \sqrt[a_4]{\cdots}}}}= \ ?

where an=3n+1a_n=3n+1. Report your answer to two decimal places.

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