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Math Help - New Cauchy question

  1. #1
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    New Cauchy question

    hello ,
    im having trouble with proving sqrt(n) is not cauchy.
    Please help.
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  2. #2
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    Quote Originally Posted by sandy View Post
    hello ,
    im having trouble with proving sqrt(n) is not Cauchy.
    Please help.
    Cauchy sequences are bounded. Is the sequence a_n=\sqrt{n} bounded?
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  3. #3
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    i need to prove it is not cauchy by using the definition
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  4. #4
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    Quote Originally Posted by sandy View Post
    i need to prove it is not cauchy by using the definition
    If n\ge 6 then \sqrt{2n}-\sqrt{n}>1
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  5. #5
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by sandy View Post
    hello please i need help proving sqrt(n) is not a cauchy sequence
    Hi. How about that it doesn't converge?
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  6. #6
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    Alternatively give me any  \epsilon>0 and N>1, then find an n>\epsilon with n>N (natural numbers are unbounded). Then  n^4>n^2>N and moreover

    |\sqrt{n^4}-\sqrt{n^2}|=|n^2-n|=|n(n-1)| \geq n > \epsilon.
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  7. #7
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    thankyo so much for you help

    thankyou to all for the help
    Last edited by mr fantastic; April 24th 2010 at 02:19 PM. Reason: Merged posts
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