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Determining of a sequence is convergent or divergence

  1. Feb 8, 2012 #1
    1. The problem statement, all variables and given/known data
    For x[itex]_{n}[/itex] given by the following formula, establish either the convergence or divergence of the sequence [itex]X = (x_{n})[/itex]

    [itex]x_{n} := (-1)^{n}n/(n+1)[/itex]


    2. Relevant equations



    3. The attempt at a solution
    This is for my real analysis class. I tried to use the squeeze theorem, but didn't get anywhere with it. I know [itex](-1)^{n}[/itex] is divergent, and n are divergent sequences but I haven't been able to use many theorems in the section because most of them are assuming something about a convergent sequence(and I need to show if it is or isn't)

    Any ideas?

    Thanks for looking


    edit:

    *Note: I have already shown that [itex]x_{n} := (-1)^{n}/(n+1)[/itex] converges to zero using the squeeze theorem, but the extra "n" in the numerator is messing me up with this one..
     
  2. jcsd
  3. Feb 8, 2012 #2

    Mark44

    Staff: Mentor

    Write out about a dozen terms in the sequence. That should give you a better idea about what this one is doing.
     
  4. Feb 8, 2012 #3
    well sure I can do that and tell that it is heading towards -1 and 1, i.e. its divergent, but I was assuming the problem was asking some kind of use of a theorem to prove its divergent
     
  5. Feb 8, 2012 #4

    Mark44

    Staff: Mentor

    You could use the definition of a divergent sequence (the negation of the definition of a convergent sequence).
     
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