Find the limit of ln(n)/ln(n+1) as n--> infinity

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SUMMARY

The limit of ln(n)/ln(n+1) as n approaches infinity is 1. The discussion highlights the application of L'Hôpital's Rule, where the expression simplifies to (1/n)/(1/(n+1)), leading to an indeterminate form of 0/0. By simplifying the complex fraction before evaluating the limit, the correct conclusion is reached that the limit converges to 1.

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can someone help me find the lim as n approaches infinity of

ln(n)/ln(n+1)

I used L'HOP so it became (1/n)/(1/n+1) -- as this approaches infinity, it's 0/0, and this confuses me. What am I doing wrong?
 
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What happens if you simplify the complex fraction

<br /> \frac{\dfrac 1 n}{\dfrac 1 {n+1}}<br />

before you evaluate the limit?
 


you are right! thanks you!
 

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