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Evaluate an Infinite Series in Closed Form

  1. Feb 28, 2009 #1
    My question is one of vocabulary. What does it mean to evaluate an infinite series in closed form?

    If I have a Series: [tex]\Sigma[/tex] 1/ (N2), as N goes from 1 to infinity.

    This is similar to a test question I'm working on so, I DO NOT want to know how to solve it, I just want to know exactly what is meant by evaluating an infinite series in closed form.
     
  2. jcsd
  3. Feb 28, 2009 #2

    Tom Mattson

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    "Expressed in closed form" means "expressed as sum of finitely many well-understood functions".

    Here's an example. Let [itex]|x|<1[/itex]. Then,

    [tex]\sum_{n=0}^{\infty}x^n=\frac{1}{1-x}[/tex]

    The expression on the left hand side is an infinite series, but the expression on the right is in closed form.
     
  4. Feb 28, 2009 #3
    Thank You!
     
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