Question

$\underset{n\to \infty }{Lt}\frac{{}^n{p}_n}{{}^{n+1}{p_{n+1}}^{{-}^n{p}_n}}=$

• A. $2$
• B. $-1$
• C. $0$
• D. $4$

Answer 1

The correct option is C $0$

Now,

$\underset{n\to \infty }{Lt}\frac{{}^n{p}_n}{{}^{n+1}{p}_{n+1}{-}^n{p}_n}$

$=\underset{n\to \infty }{Lt}\frac{n!}{(n+1)!-n!}$ [ Since ${}^n{p}_n=n!$]

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

$=\underset{n\to \infty }{lim}\frac{1}{n}$

$=0$.