Question

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

• A. 0
• B. 1
• C. -1
• D. None of these

Answer 1

The correct option is A

0

${lim}_{n\to \infty }\frac{n!}{(n+1)!-n!}$
Dividijng N' and D' by n! :
${lim}_{n\to \infty }\frac{1}{\frac{(n+1)!}{n!}-1}$
$={lim}_{n\to \infty }\frac{1}{n+1-1}$
$={lim}_{n\to \infty }=\frac{1}{n}=0$