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Where did this step come from? Problem on series converge/divergence.

  1. Apr 14, 2013 #1
    1. The original problem is this, but I'm just trying to figure out this one particular step!

    Ʃ n!/(nn)
    n=1

    2. I'm at this step:

    lim ln(n/n+1)/(1/n) = lnp
    n→∞

    BUT THEN my teacher wrote out the next step, and I'm like, "What the heck is that?!"

    This is the next step:

    lim [itex]\frac{\frac{1}{n/(n+1)}*\frac{(n+1)*1-n*1}{(n+1)^{2}}}{-1/n^{2}}[/itex]
    n→∞

    Aaaaaagh! What the heck is going on?!
    How did he get to this step? O_O

    I am stuck wondering how I am supposed to figure out the limit at: lim[itex]\frac{ln(n/(n+1)}{1/n}[/itex]!

    =_= HELP PLEASE!
    Thank you!
     
  2. jcsd
  3. Apr 14, 2013 #2
    He was applying the L'Hospital's Rule to a limit of indeterminate form 0/∞.
     
  4. Apr 14, 2013 #3

    SammyS

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    ##\displaystyle \lim_{n\to\,\infty} \left( \frac{\displaystyle \ln\left(\frac{n}{n+1}\right)}{\displaystyle \frac{1}{n}}
    \right)\ \ ## is of the indeterminate form, 0/0 .
     
  5. Apr 15, 2013 #4
    Oops, sorry, just ignore what I've said.
     
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