Nested Radicals of Geometric Sequences

Algebra Level 4

Design a formula to calculate nested radicals of the form: \(\large \sqrt[m]{1\sqrt[m]{n\sqrt[m]{n^2\sqrt[m]{n^3\cdots}}}}\)

where \(n\) is a postive real number and \(m\) is a positive integer.

Using the formula you got from previous step, the result of: \(\large \sqrt[5]{1\sqrt[5]{3\sqrt[5]{9\sqrt[5]{27\cdots}}}}\) will be in the form of \(\sqrt[x]{y}\), \(y\) is prime. What is \(x+y\)?

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