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Homework Help: Infinite limits on a sequence

  1. Apr 21, 2010 #1
    1. The problem statement, all variables and given/known data
    Well, Hi again. Here I got some limits to infinity that I don't know how to solve. The statement just ask me to calculate those limits, if exists, for the next sequences.

    [tex]\displaystyle\lim_{n \to{+}\infty}{(\sqrt[n]{n+1})}[/tex]

    [tex]\displaystyle\lim_{n \to{+}\infty}{\displaystyle\frac{\sin(n)}{n+1}}[/tex]


    [tex]\displaystyle\lim_{n \to{+}\infty}{\displaystyle\frac{1-\cos(5n)}{n^2}}[/tex]

    I don't pretend that someone solve all of these for me, but I need some orientation on which way to look. I'll be thanked for any help on any of those sequences.

    Edit: Deleted the ones that I could solve. Someone gave me some tips, and I could solve some of the limits that I have posted before. As there wasn't any responses to the topic I thought that it was unnecessary to repost giving the advertisement.
     
    Last edited: Apr 21, 2010
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  3. Apr 21, 2010 #2

    LCKurtz

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    Hints: Think about logarithms on the first and think about how big sines and cosines can be on the others.
     
  4. Apr 21, 2010 #3
    I resolved the trigonometric ones. Thanks for the hints, I'll keep working on the first.

    I established on the last two that sine and cosine are between 1 and -1, so both tend to zero.

    On the first, is this valid? [tex](\sqrt[n]{n+1})=\displaystyle\frac{log (n+1)}{n}\[/tex]
     
    Last edited: Apr 21, 2010
  5. Apr 21, 2010 #4

    LCKurtz

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    No, those two quantities aren't equal are they? But you could call

    [tex] y = \left({n+1}\right)^{\frac 1 n}[/tex]

    and then say

    [tex] \ln(y) = \frac{log (n+1)}{n}[/tex]

    and work with ln(y).
     
  6. Apr 21, 2010 #5
    Thanks, I'll remember that, because it looks like the legs of a woman (y) :D

    How did you realize that applying the ln to the expression gives the same function?

    ln(y) tends to infinite really fast. How do I get the relation between what happens with ln(y) and y?
     
    Last edited: Apr 21, 2010
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