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

  • Thread starter steven187
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  • #1
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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]

thanxs
 

Answers and Replies

  • #2
matt grime
Science Advisor
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HINT: n+1 = n(1+1/n)
 
  • #3
176
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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]
 
  • #4
yes that looks right except that you have a typo in the 3rd equation.
 

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