Infinite Tetration!

Algebra Level 2

Tetration is defined as

na=aaan a’s.\Large {^{n}a} = \underbrace{a^{a^{\cdot^{\cdot^{a}}}}}_{n \ a\text{'s}}.

Find the value of

limnn(2).\lim_{n\rightarrow\infty}{^{n}}\big(\sqrt {2}\big).

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