How Do You Calculate the Limit of a Factorial?

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The discussion focuses on calculating the limit of a factorial, with participants questioning the seriousness of the inquiry and suggesting that the asker should explore specific values like x=10 or x=1000. It emphasizes that for n greater than 2, n! is less than n^n, and n^2 is greater than n, which should clarify the limit's behavior. Additionally, a reference to evaluating the limit of n raised to the power of 1/n as n approaches infinity is mentioned. Overall, the conversation highlights the need for a deeper understanding of factorial limits and related mathematical principles.
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Please can anybody help me find this limit?
 

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It's hard to believe you are serious. Have you done anything on this yourself? Have you tried, for example, calculating values for, say, x= 10, 1000, etc.?
 
I studied the limit but not this type

this question is older than me :)
 
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Just a few things that should have made this limit quite obvious -

n! < n^n, n > 2

n^2 > n

Perhaps you have seen how to evaluate the common \lim_{n\to \infty} n^{\frac{1}{n}}?
 
Gib Z: Tanks a lot.
 

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