- #1
Lisa91
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Could anyone tell me please why the limit of this guy is infinity?
[tex] \lim_{n\to\infty} \frac{n!-1}{n^{3} \ln(n!)} [/tex]
[tex] \lim_{n\to\infty} \frac{n!-1}{n^{3} \ln(n!)} [/tex]
See what you can do with this inequality.Lisa91 said:Could anyone tell me please why the limit of this guy is infinit
[tex] \lim_{n\to\infty} \frac{n!-1}{n^{3} \ln(n!)} [/tex]
A limit problem is a mathematical concept that involves finding the value that a function approaches as its input approaches a certain value, typically infinity or negative infinity. In other words, it is finding the "limit" of a function as it gets closer and closer to a specific point.
n! (pronounced "n factorial") is a mathematical notation that represents the product of all positive integers from 1 up to and including n. For example, 5! = 1 x 2 x 3 x 4 x 5 = 120.
When solving a limit problem with n! in the equation, you can use the formula n! = n x (n-1) x (n-2) x ... x 2 x 1 to simplify the expression. Then, you can use algebraic manipulation and known limit rules to evaluate the limit.
This expression is often used in limit problems because it involves a factorial and a natural logarithm, both of which can be challenging to evaluate. It also allows for the use of various limit rules and techniques to solve the problem.
As n approaches infinity, the expression n!-1/n³ln(n!) also approaches infinity. This is because the factorial term grows much faster than the natural logarithm term, resulting in an infinitely large value.