Does the sequence converge?

Calculus Level 3

Define a sequence \(\displaystyle{\{a_n\}}_{n=1}^{\infty}\) by \[\displaystyle{a_1 = \sqrt{2}}\] \[\displaystyle{a_{n+1}} = (\sqrt{2})^{a_n},n \in N\]

Find the limit of this sequence.

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