Power Tower Sequence

Calculus Level 4

Consider the sequence

x20,x21,x22,x23,x24,x25, \Large x^{2^0}, x^{2^1}, x^{2^2}, x^{2^3}, x^{2^4}, x^{2^5} , \ldots

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

Does it converge for all complex xx with absolute value 1?


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