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Binomial Series Question

  1. Aug 5, 2009 #1
    When using a binomial series to expand [tex]1/\sqrt{1-x^{2}}[/tex] I come up with the correct answer except that I do not add the number one to my answer. Why do I have to add one to the series, should this not arise when calculating the sum?
     
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  3. Aug 5, 2009 #2

    Dick

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    If x is zero the result is 1. You should definitely have a 1 in the series. What DID you do?
     
  4. Aug 5, 2009 #3
    When expanding it I come up with the following result:

    [tex]\sum (1*3* \ldots (2n-1)*x^{2n}) / 2^{n}n! [/tex]

    According to the answer key the answer is:

    [tex]1 + \sum ((1*3* \ldots (2n-1)*x^{2n}) / 2^{n}n!) [/tex]

    Where does the one come from?
     
  5. Aug 5, 2009 #4

    Dick

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    You didn't put limits on your summations. It looks like in the books answer the limits are 1 to infinity. In your answer they are 0 to infinity. Isn't 1 the n=0 term in your series?
     
  6. Aug 6, 2009 #5
    Yes ... they separated out the [itex]n=0[/itex] term, because they thought the student would not understand the product [tex]1\cdot3\cdots(-1)[/itex]
     
  7. Aug 6, 2009 #6
    Thanks, I understand it now.
     
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