Question

$\underset{n\to \infty }{lim}\frac{(n+2)!+(n+1)!}{(n+2)!-(n+1)!}=$

• A. $1$
• B. $1/2$
• C. $-1/2$
• D. $1/3$

Answer 1

The correct option is A $1$

We divide both the numerator and the denominator, by $(n+2)!$
On simplyfying we get,

${lim}_{n\to \infty }\frac{1+\frac{(n+1)!}{(n+2)!}}{1-\frac{(n+1)!}{(n+2)!}}$

$={lim}_{n\to \infty }\frac{1+\frac{1}{(n+2)}}{1-\frac{1}{(n+2)}}$

Since, $n\to \infty ,\frac{1}{n+2}\to 0$

Applying the limit,

$=\frac{1+0}{1-0}$

$=1$