Question

${lim}_{n\to \infty }\frac{n!}{(n+1)!+n!}$ is equal to

• A. $\frac{1}{2}$
  
• B. 0
• C. 2
• D. 1

Answer 1

The correct option is B

0

${lim}_{n\to \infty }\left[\frac{n!}{(n+1)!+n!}\right]$
$={lim}_{n\to \infty }\left[\frac{n!}{(n+1)\times n!+n!}\right]$
$={lim}_{n\to \infty }\left[\frac{n!}{n!(n+1+1)}\right]$
$={lim}_{n\to \infty }\left[\frac{1}{n+2}\right]=0$