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Why doesn't this have a limit?

  1. Nov 23, 2004 #1
    Hi,

    suppose this sequence:

    [tex]
    (-1)^{n} \sqrt{n} \left( \sqrt{n+1} - \sqrt{n} \right)
    [/tex]

    I tried to find the limit and got into this point:

    [tex]
    \lim \frac{n(-1)^{n}}{ \sqrt{n(n+1)} + n}
    [/tex]

    According to results, the limit doesn't exist. But how can I find it out? Can it be visible from the point I got to?

    Thank you.
     
  2. jcsd
  3. Nov 23, 2004 #2

    matt grime

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    take the even terms, they tend to 1. take the odd terms they tend to -1
     
  4. Nov 23, 2004 #3
    Thank you matt, it's clear now. I see my approach is unnecessarilly complicated..
     
  5. Nov 23, 2004 #4

    matt grime

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    Whenever you see a (-1)^n always think about n odd and n even to see what happens.
     
  6. Nov 23, 2004 #5
    Don't they happen to tend to -1/2 or to 1/2, respectively?
     
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