# Convergence

Calculus Level 4

Initially, my calculator displays the number $$1$$. I have a button on the calculator that will replace the number it is displaying with $$n^x$$, where $$x$$ is the number previously displayed, and $$n$$ is a fixed number greater than $$1$$. What is the maximum value of $$n$$ such that, no matter how many times I press the button, the calculator will not produce an Overflow Error?

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