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N+1 = n(1+1/n) limit

  1. Jun 20, 2005 #1
    hello all

    I was workin on a problem and during my proof I came to this problem does anybody know what happens with this limit

    [tex]\lim_{n\rightarrow\infty} \frac{\log {(n+1)}}{\log {n}}[/tex]

  2. jcsd
  3. Jun 20, 2005 #2

    matt grime

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    HINT: n+1 = n(1+1/n)
  4. Jun 20, 2005 #3
    hello all

    would this be correct?

    [tex]\lim_{n\rightarrow\infty} \frac{\log {(n+1)}}{\log {n}}[/tex]
    [tex]=\lim_{n\rightarrow\infty} \frac{\log {n(1+\frac{1}{n})}}{\log {n}}[/tex]
    [tex]=\lim_{n\rightarrow\infty} \frac{\log{n}+\log {n(1+\frac{1}{n})}}{\log {n}}[/tex]
    [tex]=1+\lim_{n\rightarrow\infty} \frac{\log {(1+\frac{1}{n})}}{\log {n}}=1[/tex]
  5. Jun 20, 2005 #4
    yes that looks right except that you have a typo in the 3rd equation.
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