Can It Converge?
Consider the infinite tetration
What is the upper bound value of for which this expression converges?
Bonus: Establish a lower bound.
The answer is 1.444667861.
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1 solution
首先，令x=(t^(1/t)),式子收敛,然后再对x求导，得到x'=(－1)ln(t)t^(－2)t^(1/t)+t^(-2)t^(1/t), 令x'=0, so t=e^(1/e)=1.44466786