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Math Help - Taylor Series

  1. #1
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    Taylor Series

    Compute the Taylor series of (1-x)^(-1/2) by Taylor's formula.


    I used Taylor's formula to get the first few terms but couldn't see a reasonable pattern to generalize...

    Any help at all is appreciated
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  2. #2
    Super Member PaulRS's Avatar
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    Try proving the general case.

    Given a real number u and a natural number n we define: \binom{u}{n}=\frac{u\cdot{(u-1)\cdot{...\cdot{(u-n+1)}}}}{n!}

    The Binomial Theorem states that:

    (1+x)^u=\sum_{n=0}^{\infty}{\binom{u}{n}\cdot{x^n}  }

    |x|<1

    Note that if u is natural then the formula reduces to the famous: (1+x)^u=\sum_{n=0}^{u}{\binom{u}{n}\cdot{x^n}}


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  3. #3
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Please don't double post

    http://www.mathhelpforum.com/math-he...or-series.html

    Please don't double post

    It just makes more work for everyone.

    I gave you the formual for the nth derivative(The long way)

    Try it and see what happens
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  4. #4
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    Quote Originally Posted by TheEmptySet View Post
    http://www.mathhelpforum.com/math-he...or-series.html

    Please don't double post

    It just makes more work for everyone.

    I gave you the formual for the nth derivative(The long way)

    Try it and see what happens
    I'm sorry . It won't happen again.
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