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Example of cauchy sequence

  1. Oct 14, 2013 #1
    one of example of cauchy sequence show that

    = 1/n - 1/(n+k)

    and In the above we have used the inequality

    1/(n+m)^2 <= ( 1/(n+m-1) - 1/(n+m) ) => i don't under stand where this come from

    and what is inequality? can you give other example?
     
    Last edited by a moderator: Oct 14, 2013
  2. jcsd
  3. Oct 14, 2013 #2

    jbunniii

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    $$\frac{1}{n+m-1} - \frac{1}{n+m} = \frac{1}{(n+m-1)(n+m)}$$
    Assuming ##n## and ##m## are positive, it's clear that the right hand side is larger than ##1/(n+m)^2##, because ##n+m-1 < n+m##.
     
  4. Oct 15, 2013 #3
    I'm not very clear about what the question is. Do you need to know how to prove the sequence is Cauchy? Do you need to understand what an inequality is?
     
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