1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Limit of ln(n)/ln(n+1) as n->+infinity, very confusing

  1. Oct 26, 2008 #1
    Limit of ln(n)/ln(n+1) as n-->+infinity, very confusing

    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?
     
  2. jcsd
  3. Oct 26, 2008 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    Re: L'hop

    [itex]\frac{d}{dn} ln(n+1)=\frac{1}{n+1} \neq \frac{1}{n}+1[/itex]

    Does that help ? ;0)
     
  4. Oct 27, 2008 #3
    Re: L'hop

    first, [tex]\frac{\frac{1}{n}}{\frac{1}{1+n}}=\frac{1+n}{n}=1+\frac{1}{n}[/tex] which approaches to 1, as n approaches to infinity...
    second, I'm assuming n stands for integers. And L'hospitals Rule is not allowed to apply to a sequence.
     
    Last edited: Oct 27, 2008
  5. Oct 27, 2008 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: L'hop

    L'Hopitals Rule certainly is allowed to apply to a sequence! If f(x) has limit L as x goes to infinity then f(n) has limit L as n goes to infinity. This method is perfectly valid. Of course, you have to do the derivative and the algbra correctly!
     
  6. Oct 27, 2008 #5
    Re: L'hop

    yeah, I mean this exactly, but applying L'hospitals by brute force is not proper (derivative can be applyed to x but not to n).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?