Does the sequence converge?

Calculus Level 3

Define a sequence {an}n=1\displaystyle{\{a_n\}}_{n=1}^{\infty} by a1=2\displaystyle{a_1 = \sqrt{2}} an+1=(2)an,nN\displaystyle{a_{n+1}} = (\sqrt{2})^{a_n},n \in N

Find the limit of this sequence.

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