Just another tetration.

Calculus Level 4

\[\displaystyle {x=e^ {(e^{-1})^{e^{(e^{-1})^{...}}}}}\]

\[\text{Find } x \text{.}\]

Details and assumptions

\[\text{If you can't read the expression, it's an alternating}\] \[\text{infinite tetration, with the terms being } e \text{ and } {e}^{-1} \text{.}\]

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