Evaluate: _ n n! (n+1)!-n! - Vidyadip

MCQ

Evaluate: $\lim_{\text{n} \rightarrow \infty} \dfrac{\text{n}!}{(\text{n}+1)!-\text{n}!}$

✓
$0$
B
$1$
C
$2$
D
$3$

✓

Answer

Correct option: A.

$0$

We have,$\lim\limits_{\text{n} \rightarrow \infty} \dfrac{\text{n}!}{(\text{n}+1)!-\text{n}!}$
$=\lim\limits_{\text{n} \rightarrow \infty} \dfrac{\text{n}!}{(\text{n}+1)\text{n}!-\text{n}!}$
$ =\lim\limits_{\text{n}\rightarrow \infty} \dfrac{1}{\text{n}+1-1}$
$ =\lim\limits_{\text{n}\rightarrow \infty}\frac{1}{\text{n}}=0$

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