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Does $\sqrt[x!]{x}$ converge? If yes, to what?

I couldn't find any solutions to it. If anybody could show to what it converges or diverges, then I would appreciate it!

Angelo
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Csoriburi
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  • What is your function? It's hard to parse. Are you defining $x!$ via the Gamma function when $x\not \in \mathbb N$? Something else? – lulu Feb 28 '23 at 18:16
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    Welcome to [math.se] SE. Take a [tour]. You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an [edit]): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance. – Another User Feb 28 '23 at 18:17
  • In this case I thought of it as x an integer. – Csoriburi Feb 28 '23 at 18:18

1 Answers1

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Hint: the answer is $1$. This can be easily proven by using the identity $f(x)=e^{\ln(f(x))}$

b00n heT
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