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Math Help - Last Taylor series question for awhile, promise

  1. #1
    Junior Member
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    Last Taylor series question for awhile, promise

    Ok, so my function is f(x)=\frac{1}{(1+x^2)^{1/3}} and I'm supposed to approximate the integral for it. I can do that once I have the power series easily enough since the instructions are to get a sixth-degree Taylor polynomial, which I can do if I know the power series, and then it's just a matter of plug and chug....now, I can do the derivatives for this and find the pattern, but it'll get extremely ugly after the first derivative, so is there a way to use an elementary power series on this problem so I can avoid having to do the 2nd, 3rd, etc. derivatives by parts?
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    What you have to do here it is to use for |x|<1,\,(1+x)^\alpha=\sum_{k\,=\,0}^\infty\binom{\  alpha}{k}x^k where \binom{\alpha}{k}=\frac{\alpha(\alpha-1)(\alpha-2)\cdots(\alpha-k+1)}{k!}.
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    But in this case

    doesnt it need to be (1+x^2)^\alpha?
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