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Math Help - Infinite Limit Question

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    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|?
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    Quote Originally Posted by kaiser0792 View Post
    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|
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    Nice, thank you!
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  4. #4
    MHF Contributor matheagle's Avatar
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    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|
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