Question

The value of $\underset{n\to \infty }{\lim }\frac{n!}{(n+1)!-n!}$ is

Answer 1

$\underset{n\to \infty }{\lim }\frac{n!}{(n+1)!-n!}=\underset{n\to \infty }{\lim }\frac{n!}{(n+1)\cdot n!-n!}=\underset{n\to \infty }{\lim }\frac{n!}{n!\left(n+1-1\right]}=\underset{n\to \infty }{\lim }\frac{1}{n}=0$