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Partial Sum and Complete Sum

  1. Feb 17, 2010 #1
    Is there a particular way to get the partial sum easier than just adding the terms up?

    In this formula it would take a while to add up the terms if I wanted to use n=20:

    [tex] S_{n}+\int ^{\infty}_{n+1}f(x) dx\leqs\leq S_{n}+\int ^{\infty}_{n}f(x)dx [/tex]

    How would I get the exact value of the sum?
     
  2. jcsd
  3. Feb 17, 2010 #2

    mathman

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    You haven't defined what the terms in the sum are, so there is no way of knowing what can be done.
     
  4. Feb 17, 2010 #3
    Oh, I though that there was something like a formula that could be used in general cases. So I'll use the example:

    [tex]\sum^{\infty}_{n=0} \frac{(-1)^{n}x^{2n}}{n!}[/tex]
     
  5. Feb 18, 2010 #4

    mathman

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    For the particular example the sum is exp(-x2). For this case, there is no way to get partial sums except by direct addition.
     
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