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Binomial Series Question

  • Thread starter paridiso
  • Start date
  • #1
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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?
 

Answers and Replies

  • #2
Dick
Science Advisor
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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?
 
  • #3
17
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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?
 
  • #4
Dick
Science Advisor
Homework Helper
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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?
 
  • #5
607
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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]
 
  • #6
17
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Thanks, I understand it now.
 

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