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Taylor series with summation notation

  1. Jun 4, 2009 #1
    1. The problem statement, all variables and given/known data

    f(x) = [tex]\frac{1-cos(X^2)}{x^3}[/tex]

    which identity shoud i use?
    and tips on this type of questions? once i can separate them, then i'll be good


    thanks!
     
  2. jcsd
  3. Jun 4, 2009 #2

    benorin

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    Do you know a Taylor series for [itex]\cos x[/itex]?
     
  4. Jun 4, 2009 #3
    yeah, but there's a x^3 on the bottom...
     
  5. Jun 4, 2009 #4

    Cyosis

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    Sure, but the summation isn't over x so you can put the x in the sum or outside the sum.
     
  6. Jun 15, 2009 #5

    benorin

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    Example:

    [tex]\frac{1-\sin 2x^3}{x}=\frac{1-\sum_{k=0}^{\infty}\frac{\left( 2x^3\right)^{2k+1}}{(2k+1)!}}{x} = {\scriptstyle \frac{1}{x}}-{\scriptstyle \frac{1}{x}}\sum_{k=0}^{\infty}\frac{2^{2k-1}x^{6k+3}}{(2k+1)!}[/tex]
    = {\scriptstyle \frac{1}{x}}-\sum_{k=0}^{\infty}\frac{2^{2k-1}x^{6k+2}}{(2k+1)!}[/tex]​
     
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