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Alternating Series Help

  1. Nov 21, 2005 #1
    I apologize right now for the fact that I have no idea how to use LaTeX

    I can't figure out if the following alternating series is convergent or not:

    Sum(((-1)^(n-1)) * ((2n+1)/(n+2))) from 1 to infinity

    the root test is not applicable, A(n+1)>An, and the ratio test gives me Limit=1, so I have no comclusive evidence either way. Even Maple 10 couldnt give me an answer.
    I have a test tomorrow. HELP!!!!!!!
     
  2. jcsd
  3. Nov 21, 2005 #2
    Did you try the alternating series test?
     
  4. Nov 21, 2005 #3

    uart

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    Just take a look at the limiting terms in that series. As n goes to infinity the absolute value of the terms goes to two, so alternating or not there is no way it can converge.
     
  5. Nov 21, 2005 #4

    uart

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    BYW. I'm petty sure you can show that the above series is bounded, that is that it doesn't creep off to +/- infinity, but it definitely doesn't converge to a well defined limit point.
     
  6. Nov 22, 2005 #5

    HallsofIvy

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    You are aware, are you not, that is an does not go to zero, then the series[itex]\Sigma a_n[/itex] cannot converge? That's normally the very first "series" property you learn!
     
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