Power Tower Sequence

Calculus Level 4

Consider the sequence

\[ \Large x^{2^0}, x^{2^1}, x^{2^2}, x^{2^3}, x^{2^4}, x^{2^5} , \ldots \]

If \( |x| < 1 \), then this sequence converges for all real and complex \(x\).
If \( x = 1, -1 \), then this sequence also converges.

Does it converge for all complex \(x\) with absolute value 1?

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