# 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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