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Convergence - Divergence of a Series

  1. Apr 10, 2009 #1
    1. The problem statement, all variables and given/known data
    Test the series for convergence or divergence
    -1/3+ 2/4 - 3/5 +4/6 - 5/7 + .................


    2. Relevant equations

    I think it's an alternating series

    3. The attempt at a solution

    I found that an = (-1) ^n * n/ (n+2)

    And it approaches 1 as n goes to inifty so the series will Diverge

    Is that right ??
     
  2. jcsd
  3. Apr 10, 2009 #2
    hmmm.
    alternating series test says that if you can identify a series of the form [itex]\sum (-1)^n a_n[/itex] and the [itex]a_n[/itex] are positive and decreasing such that [itex]a_n \rightarrow 0[/itex] then [itex]\sum (-1)^n a_n[/itex] will converge.

    so here you have [itex]a_n=\frac{n}{n+2}=\frac{1}{1+\frac{2}{n}}[/itex]

    how does this behave as [itex]n \rightarrow \infty[/itex]
     
  4. Apr 11, 2009 #3
    It will approach 1. and the series will Diverge.

    What do you think ?
     
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