Hi there!
We are given the function -
[tex] \lim_{n \to \infty} \frac{(n+1)!}{n!-(n+1)!}[/tex]
and are told to find the limit of the function.
The limit would be n approaches infinity, giving us an answer of -1.
Here is how you solve this:
[tex]\frac{(n+1)!}{n!-(n+1)!}[/tex]
Divide by (n + 1)! -
[tex] \frac{1}{\frac{1}{n+1}-1 } [/tex]
Now, we can refine the function -
[tex] \lim_{n \to \infty}\frac{1}{\frac{1}{n+1}-1 } [/tex]
Now, just simplify. This gives us -
[tex] \lim_{n \to \infty} (1)[/tex]
We can use the rule [tex] \lim_{x \to a}c=c[/tex] to simplify the whole thing to get 1. Finally, we plug it back into our second derived equation to get 1/-1, which simplifies to -1. Therefore, the answer is -1. Hope this helped and have a great day!
