Let $F_n$ be the $n$th Fermat number $2^{2^n}+1$.Find $$\lim_{n\rightarrow\infty}\sqrt{6F_1+\sqrt{6F_2+\sqrt{6F_3+\sqrt{\cdots +6F_n}}}}.$$ This is The American Mathematical Monthly problem 11967. I think it's so difficult that I have no ideal.
2026-03-30 08:11:36.1774858296
Infinitely nested radicals problem about Fermat number
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