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Math Help - Binomial Expansion

  1. #1
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    Binomial Expansion

    Can someone remind me which Binomial Expansion formula is used to expand:

     \frac{1}{1+x^2} = 1 + (-1)x^2 + \frac{(-1)(-2)}{2!}(x^2)^2 + \frac{(-1)(-2)(-3)}{3!}(x^2)^3+...

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by Air View Post
    Can someone remind me which Binomial Expansion formula is used to expand:

     \frac{1}{1+x^2} = 1 + (-1)x^2 + \frac{(-1)(-2)}{2!}(x^2)^2 + \frac{(-1)(-2)(-3)}{3!}(x^2)^3+...

    Thanks in advance.
    You can do it much easier using the sum of an infinite geometric series formula:

    1 + r + r^2 + \, .... = \frac{1}{1 - r}

    (provided |r| < 1).

    In your case r = -x^2.
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  3. #3
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    If you really want to do it using the (generalized) binomial expansion, do it as (a+ 1)^n with a= x^2 and n= -1.
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