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Taylor series representation help

  1. May 21, 2014 #1
    1. The problem statement, all variables and given/known data
    Find the Taylor Series of x^(1/2) at a=1


    2. Relevant equations
    i have no idea how to do the representation, i believe our professor does not want us to use any binomial coefficients


    3. The attempt at a solution
    i got the expansion and heres my attempt at the representation

    1+∑(1 to ∞) [(-1)(-3)...(-(2n+1))/2^n](x-1)^n/(n!)
     
  2. jcsd
  3. May 21, 2014 #2

    HallsofIvy

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    There are many different ways to "represent" a function as a series but the definition of the "Taylor series" representation of f(x) is
    [tex]\sum_{n=0}^\infty \frac{f^{(n)}(a)}{n!}(x- a)^n[/tex]
    where "[itex]f^{(n)}(a)[/itex]" is the nth derivative of f at x= a. Have you found the nth derivative of [itex]x^{1/2}[/itex]?
     
    Last edited by a moderator: May 21, 2014
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