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Convergance and Divergence Could someone go over a routine to help determine them?

  1. Oct 14, 2011 #1
    Hey there..

    Basically I'm struggling with convergence and divergence of series.

    I can see if converges and diverges by common sense and thinking through in my head but I struggle to write it down. The definitions in books seem confusing.

    Are there any steps I can systematically do every time which will help me determine on paper if the said series div. or conv.?

    For example a basic typical question in my course is like the following:

    as n ---> infinity

    [itex]\sum[/itex] (n^2 - 1) / (n^4 + 1)

    Some detailed exlanation in basic language would be greatly appreciated

  2. jcsd
  3. Oct 14, 2011 #2
    Re: Convergance and Divergence.. Could someone go over a routine to help determine th

    There are many different tools to test the convergence of a series, the most common probably being the comparison test, the integral test, the ratio test, and the nth root test. Here's a link with a big list: http://www.math.hmc.edu/calculus/tutorials/convergence/

    In your particular example, I think comparison with the series [itex] \sum_{n=1}^\infty \frac{1}{n^2}[/itex] is the easiest test to use.
  4. Oct 15, 2011 #3
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