# 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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