Question

Please 29%21%7D" id="TexFormula1" title=" \lim_{n \to \infty} \frac{(n+1)!}{n!-(n+1)!}" alt=" \lim_{n \to \infty} \frac{(n+1)!}{n!-(n+1)!}" align="absmiddle" class="latex-formula">

Answer 1

Hi there!
We are given the function - 
$\lim_{n \to \infty} \frac{(n+1)!}{n!-(n+1)!}$
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:
$\frac{(n+1)!}{n!-(n+1)!}$
Divide by (n + 1)! - 
$\frac{1}{\frac{1}{n+1}-1 }$
Now, we can refine the function - 
$\lim_{n \to \infty}\frac{1}{\frac{1}{n+1}-1 }$
Now, just simplify. This gives us - 
$\lim_{n \to \infty} (1)$
We can use the rule $\lim_{x \to a}c=c$ 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!