1. ## Infinite Limit Question

Can anyone please explain to me how $\lim_{n->\infty}\left| \frac{nx}{n+1} \right| = |x|$? Does it not require L' Hopital's Rule and if so, how does it evaluate to |x|?

2. Originally Posted by kaiser0792
Can anyone please explain to me how $\lim_{n->\infty}\left| \frac{nx}{n+1} \right| = |x|$? Does it not require L' Hopital's Rule and if so, how does it evaluate to |x|?
$\left| \frac{nx}{n+1} \right|=\bigg|\frac{n}{n} \bigg|\left| \frac{x}{1+\frac{1}{n}} \right| = \left| \frac{x}{1+\frac{1}{n}} \right|$

3. Nice, thank you!

4. I'd pull out the |x| since n is certainly positive.

$\left | \frac{nx}{n+1} \right| = |x|\left({n\over n+1}\right)\to |x|\cdot 1=|x|$