The value of lim_{n to infty} frac{(n + 2)! + | vedclass

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Question

(C) Step $1$: Simplify the expression by factoring out $(n + 1)!$ from the numerator and denominator.$\frac{(n + 2)! + (n + 1)!}{(n + 2)! - (n + 1)!}

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(C) Step $1$: Simplify the expression by factoring out $(n + 1)!$ from the numerator and denominator.$\frac{(n + 2)! + (n + 1)!}{(n + 2)! - (n + 1)!} = \frac{(n + 1)! 	imes (n + 2 + 1)}{(n + 1)! 	imes (n + 2 - 1)}$Step $2$: Cancel the common term $(n + 1)!$.$= \frac{n + 3}{n + 1}$Step $3$: Divide the numerator and denominator by $n$.$= \frac{1 + \frac{3}{n}}{1 + \frac{1}{n}}$Step $4$: Apply the limit as $n 	o \infty$.$\lim_{n 	o \infty} \frac{1 + \frac{3}{n}}{1 + \frac{1}{n}} = \frac{1 + 0}{1 + 0} = 1$

The value of $\lim_{n \to \infty} \frac{(n + 2)! + (n + 1)!}{(n + 2)! - (n + 1)!}$ is

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