Find Limit of Factorial: Help Needed

In summary, the factorial of a positive integer n, denoted by n!, is the product of all positive integers from 1 up to n. Finding the limit of a factorial is important in many areas of mathematics, including calculus, probability, and combinatorics, as it allows us to solve problems involving infinite sequences and series and analyze the growth rate of functions. The general procedure for finding the limit of a factorial involves rewriting it in terms of exponential and logarithmic functions and then applying various limit rules and identities. The limit of a factorial can only be 0 or infinity, and there are two special cases to consider: the limit of 0! and the limit of (n!)^(1/n) as n approaches infinity, both
  • #1
joghurt
2
0
Please can anybody help me find this limit?
 

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  • #2
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.?
 
  • #3
I studied the limit but not this type

this question is older than me :)
 
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  • #4
Just a few things that should have made this limit quite obvious -

[tex]n! < n^n, n > 2[/tex]

[tex]n^2 > n[/tex]

Perhaps you have seen how to evaluate the common [tex]\lim_{n\to \infty} n^{\frac{1}{n}}[/tex]?
 
  • #5
Gib Z: Tanks a lot.
 

1. What is the definition of factorial?

The factorial of a positive integer n, denoted by n!, is the product of all positive integers from 1 up to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

2. Why is it important to find the limit of a factorial?

Finding the limit of a factorial is important in many areas of mathematics, including calculus, probability, and combinatorics. It allows us to solve problems involving infinite sequences and series, as well as analyze the growth rate of functions.

3. What is the procedure for finding the limit of a factorial?

The general procedure for finding the limit of a factorial is to first rewrite it in terms of exponential and logarithmic functions, then apply various limit rules and identities to simplify the expression. Finally, take the limit as the variable approaches infinity to determine the final answer.

4. Can the limit of a factorial be any value?

No, the limit of a factorial can only be 0 or infinity. It is not possible for the limit to be a finite number.

5. Are there any special cases when finding the limit of a factorial?

Yes, there are two special cases when finding the limit of a factorial: the limit of 0! and the limit of (n!)^(1/n) as n approaches infinity. In both cases, the limit is equal to 1.

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